Universal nonlinear dynamics in damped and driven physical systems: From Pendula via Josephson junctions to power grids
Chittaranjan Hens
Physics Reports, Phy R, 2025
@inproceedings{bib_Univ_2025, AUTHOR = {Hens, Chittaranjan }, TITLE = {Universal nonlinear dynamics in damped and driven physical systems: From Pendula via Josephson junctions to power grids}, BOOKTITLE = {Physics Reports}. YEAR = {2025}}
Understanding the collective behavior of dynamical systems is essential for explaining various emergent phenomena in natural and engineered settings. A key step in this process is formulating an appropriate mathematical description of the individual systems and network of systems. In this context, a range of physical systems is considered here, including the classical pendula, superconducting Josephson junctions, power grids, and various others. Despite the diversity of the systems in terms of physical structure and their application domains, they exhibit strikingly similar dynamical features, namely, phase dynamics governed by inertia and damping, and in their response to external forcing. This observation creates interest and motivates a search for a unified theoretical framework capable of capturing the fundamentals of their dynamical behaviors exhibited across the systems. This review critically examines the up-to-date research activities on the dynamics of the second-order phase oscillator, henceforth claimed here as a universality class by its own merits as a simple nonlinear dynamical model representing a broad class of physical systems. It offers a common mathematical framework to develop a comprehensive understanding, from a general perspective, that bridges, the theoretical and experimental observations of pendulum motion, Josephson junctions, and power grids and their collective behaviors. While each of these systems has been discussed in disparate physical contexts, their underlying mathematical structures reveal strong commonalities. In particular, we highlight the importance of analyzing these systems through the lens of nonlinear phase dynamics to uncover their shared mechanisms and system-specific variety of behaviors as well. This survey mainly focuses on some specific interrelated themes: (i) collective phenomena and emergent synchronization; (ii) the role of heterogeneity in terms of system parameters and effects of noise on the emergent dynamics; (iii) multi-stability and complex transient regimes; (iv) the integration of machine learning for model discovery, control, and prediction; and (v) the broader applicability of phase oscillator models across diverse domains beyond the canonical systems considered here. By systematically comparing the dynamical behaviors of the varied physical systems within a cohesive mathematical framework of second-order phase oscillators, this review seeks for the universal and distinctive features of nonlinear dynamics of the three systems, their collective behaviors such as emergent synchrony, partial synchrony, or chimera states, and specifically explains real-life phenomena, and crowd synchrony that may lead to a collapse of a footbridge and the failure of a power grid. Besides our main emphasis on these systems, brief notes have been added on other systems where this second-order phase model explains their dynamical properties. A broad synthesis on the topic will not only deepen our theoretical understanding but also suggest any design and control of complex dynamical systems in both natural and engineered settings.
Generalized Adaptation-Induced Non-universal Synchronization Transitions in Random Hypergraphs
Chittaranjan Hens
@inproceedings{bib_Gene_2025, AUTHOR = {Hens, Chittaranjan }, TITLE = {Generalized Adaptation-Induced Non-universal Synchronization Transitions in Random Hypergraphs}, BOOKTITLE = {Chaos}. YEAR = {2025}}
We investigate the effect of partial order parameter adaptation in the form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are considered pairwise and triangular. Using the Ott–Antonsen ansatz, we obtain a set of self-consistent equations of the order parameter that describe the synchronization patterns. A broad diversity of synchronization transitions is observed as a result of the interplay between the partial adaptation approach, generalized adaptation functions, and coupling strengths. The system specifically shows a double-jump transition under a power law form of the adaptation function. A polynomial form of the adaptation function leads to the emergence of an intermediate synchronization state for specific combinations of one negative and one positive coefficient. Moreover, the synchronization transition may become continuous or explosive when the pairwise coupling strength varies. This type of synchronization behavior is further found by using a Gaussian adaptation function.
A compounded Burr probability distribution for fitting heavy-tailed data with applications to biological networks
Chittaranjan Hens,Sangita Dutta
@inproceedings{bib_A_co_2025, AUTHOR = {Hens, Chittaranjan and Dutta, Sangita }, TITLE = {A compounded Burr probability distribution for fitting heavy-tailed data with applications to biological networks}, BOOKTITLE = {Chaos}. YEAR = {2025}}
Complex biological networks, encompassing metabolic pathways, gene regulatory systems, and protein–protein interaction networks, often exhibit scale-free structures characterized by heavy-tailed degree distributions. However, empirical studies reveal significant deviations from ideal power-law behavior, underscoring the need for more flexible and accurate probabilistic models. In this work, we propose the Compounded Burr (CBurr) distribution, a novel four-parameter family derived by compounding the Burr distribution with a discrete mixing process. This model is specifically designed to capture both the body and tail behavior of real-world network degree distributions with applications to biological networks. We rigorously derive its statistical properties, including moments, hazard and risk functions, and tail behavior, and develop an efficient maximum likelihood estimation framework. The CBurr model demonstrates broad applicability to networks with complex connectivity patterns, particularly in biological, social, and technological domains. Extensive experiments on large-scale biological network datasets show that CBurr consistently outperforms classical power-law, lognormal, and other heavy-tailed models across the full degree spectrum. By providing a statistically grounded and interpretable framework, the CBurr model enhances our ability to characterize the structural heterogeneity of biological networks.
Teleportation fidelity of quantum repeater networks
M Ganesh,Subrata Ghosh,Chittaranjan Hens,Indranil Chakrabarty,Subhadip Mitra
Physical Review A, PRA, 2025
@inproceedings{bib_Tele_2025, AUTHOR = {Ganesh, M and Ghosh, Subrata and Hens, Chittaranjan and Chakrabarty, Indranil and Mitra, Subhadip }, TITLE = {Teleportation fidelity of quantum repeater networks}, BOOKTITLE = {Physical Review A}. YEAR = {2025}}
We show that the average of the maximum teleportation fidelities between all pairs of nodes in a large quantum
repeater network is a measure of the resourcefulness of the network as a whole. It can be used to rank networks
of arbitrary topologies, with and without loops. For demonstration purposes, we use simple Werner state-based
models to characterize some fundamental topologies (the star, the chain, some trees, and also the ring and the
complete graph) with this measure in three (semi)realistic scenarios. Most of our results are analytic and apply to
arbitrary network sizes. We identify the parameter ranges where these networks can achieve quantum advantages
and show the large-N behaviors.
Pattern change of precipitation extremes in Svalbard
Dhiman Das,R.Athulya,Tanujit Chakraborty,Arnob Ray,Chittaranjan Hens,Syamal K. Dana,DibakarGhosh,Nuncio Murukesh
Scientific Reports, SR, 2025
Abs | | bib Tex
@inproceedings{bib_Patt_2025, AUTHOR = {Das, Dhiman and R.Athulya, and Chakraborty, Tanujit and Ray, Arnob and Hens, Chittaranjan and Dana, Syamal K. and DibakarGhosh, and Murukesh, Nuncio }, TITLE = {Pattern change of precipitation extremes in Svalbard}, BOOKTITLE = {Scientific Reports}. YEAR = {2025}}
Besides global attention on extreme precipitation, a limited research has been done in the Arctic due to constraints of data availability. In this backdrop, we attempt to analyze extreme precipitation events at three Arctic stations (Bjørnøya, Ny-Ålesund, and Svalbard Lufthavn) in Svalbard using extreme value theory. The analysis revealed that these high-latitudinal Arctic stations were characterized by heavy-tailed distributions for the exceedances, suggesting a higher probability of the occurrence of extreme precipitation events. Ny-Ålesund and Bjørnøya have exhibited a significant increase in return values over the last three decades. Among the three stations, Ny-Ålesund displayed the strongest return values, especially in winter post-1994 when the atmospheric temperature was characterized by an enhanced positive trend. Significant seasonal variability in return values has also been observed; the fall in Ny-Ålesund was characterized by a low-intensity regime as indicated by the shape parameter. Ny-Ålesund precipitation had shifted from heavy-tailed distribution in pre-1994 to bounded tail distribution post-1994 during spring. Bjørnøya’s extremes are driven by cyclonic circulation, while southerly winds drive extremes in Ny-Ålesund and Svalbard Lufthavn. Even though, Svalbard Lufthavn, displayed regime changes, showed low variability, likely due to its position in a rain shadow region. This research highlights the nuanced responses of Arctic hydrology to warming, emphasizing the need for localized studies and active collaboration with policymakers to translate these insights into effective climate adaptation and mitigation strategies.
Topological phase transition in antisymmetric Lotka-Volterra doublet chain
Rukmani Bai,Sourin Chatterjee,Ujjwal Shekhar,Abhishek Deshpande,Sirshendu Bhattacharyya,Chittaranjan Hens
Physical Review E, PRE, 2025
@inproceedings{bib_Topo_2025, AUTHOR = {Bai, Rukmani and Chatterjee, Sourin and Shekhar, Ujjwal and Deshpande, Abhishek and Bhattacharyya, Sirshendu and Hens, Chittaranjan }, TITLE = {Topological phase transition in antisymmetric Lotka-Volterra doublet chain}, BOOKTITLE = {Physical Review E}. YEAR = {2025}}
We present the emergence of topological phase transition in the minimal model of two-dimensional rockpaper-
scissors cycle in the form of a doublet chain. The evolutionary dynamics of the doublet chain is obtained
by solving the anti-symmetric Lotka-Volterra equation. We show that the mass decays exponentially towards
edges and robust against small perturbation in the rate of change of mass transfer, a signature of a topological
phase. For one of the configuration of our doublet chain, the mass is transferred towards both edges and the bulk
is gaped. Further, we confirm this phase transition within the framework of topological band theory. For this,
we calculate the winding number, which change from zero to one for trivial and nontrivial topological phases,
respectively.
Analyzing epidemiological trends in second and third waves of COVID-19 variants in India
Kushagra Agarwal,Subrata Ghosh,Nita Parekh,Chittaranjan Hens
The European Physical Journal Special Topics, EPJST, 2024
@inproceedings{bib_Anal_2024, AUTHOR = {Agarwal, Kushagra and Ghosh, Subrata and Parekh, Nita and Hens, Chittaranjan }, TITLE = {Analyzing epidemiological trends in second and third waves of COVID-19 variants in India}, BOOKTITLE = {The European Physical Journal Special Topics}. YEAR = {2024}}
The COVID-19 pandemic wrought havoc across India, particularly during its devastating second and third waves. This study undertakes a crucial epidemiological analysis of these waves, leveraging actual variant count data. Given limited sequencing efforts, variant information is sparse, prompting a novel approach to scaling up with actual case data. Employing a multi-strain variant-level SEIRS model tailored to each Indian state, we modeled the disease’s propagation. We report the estimated parameters of the SEIRS models for the two waves separately. Notably, the transmission coefficients (
) were estimated to be 0.12 for Kappa, 0.35 for Delta, and 0.38 for Omicron. These coefficients signify the contagiousness of each variant, offering critical information for understanding and managing the pandemic’s dynamics. The findings hold significant implications for public health strategies, emphasizing the urgency of comprehensive variant tracking and proactive measures to mitigate the impact of evolving viral strains.
Coprime networks of the composite numbers: Pseudo-randomness and synchronizability
Md Rahil Miraj,Dibakar Ghosh,Chittaranjan Hens
Discrete Applied Mathematics, DAM, 2024
@inproceedings{bib_Copr_2024, AUTHOR = {Miraj, Md Rahil and Ghosh, Dibakar and Hens, Chittaranjan }, TITLE = {Coprime networks of the composite numbers: Pseudo-randomness and synchronizability}, BOOKTITLE = {Discrete Applied Mathematics}. YEAR = {2024}}
In this paper, we propose a network whose nodes are labeled by the composite numbers
and two nodes are connected by an undirected link if they are relatively prime to each
other. As the size of the network increases, the network will be connected whenever
the largest possible node index n ≥ 49. To investigate how the nodes are connected, we
analytically describe that the link density saturates to 6/π2
, whereas the average degree
increases linearly with slope 6/π2 with the size of the network. To investigate how the
neighbors of the nodes are connected to each other, we find the shortest path length
will be at most 3 for 49 ≤ n ≤ 288 and it is at most 2 for n ≥ 289. We also derive
an analytic expression for the local clustering coefficients of the nodes, which quantifies
how close the neighbors of a node to form a triangle. We also provide an expression for
the number of r-length labeled cycles, which indicates the existence of a cycle of length
at most O(log n). Finally, we show that this graph sequence is actually a sequence of
weakly pseudo-random graphs. We numerically verify our observed analytical results.
As a possible application, we have observed less synchronizability (the ratio of the
largest and smallest positive eigenvalue of the Laplacian matrix is high) as compared to
Erdős–Rényi random network and Barabási–Albert network. This unusual observation
is consistent with the prolonged transient behaviors of ecological and predator–prey
networks which can easily avoid the global synchronization.
Transition to synchronization in the adaptive Sakaguchi-Kuramoto model with higher-order interactions
Sangita Dutta,Prosenjit Kundu,Pitambar Khanra,Chittaranjan Hens,Pinaki Pal
Physical Review E, PRE, 2024
@inproceedings{bib_Tran_2024, AUTHOR = {Dutta, Sangita and Kundu, Prosenjit and Khanra, Pitambar and Hens, Chittaranjan and Pal, Pinaki }, TITLE = {Transition to synchronization in the adaptive Sakaguchi-Kuramoto model with higher-order interactions}, BOOKTITLE = {Physical Review E}. YEAR = {2024}}
We investigate the phenomenon of transition to synchronization in the Sakaguchi-Kuramoto model in the presence of higher-order interactions and global order parameter adaptation. The investigation is done by performing extensive numerical simulations and low-dimensional modeling of the system. Numerical simulations of the full system show both continuous (second-order) as well as discontinuous transitions. The discontinuous transitions can either be associated with explosive (first-order) or tiered synchronization states depending on the choice of parameters. To develop an in depth understanding of the transition scenario in the parameter space we derive a reduced order model (ROM) using the Ott-Antonsen ansatz, the results of which closely match with those of the numerical simulations of the full system. The simplicity and analytical accessibility of the ROM help to conveniently unfold the transition scenario in the system having complex dependence on the parameters. Simultaneous analysis of the full system and the ROM clearly identifies the regions of the parameter space exhibiting different types of transitions. It is observed that the second-order transition is connected with a supercritical pitchfork bifurcation (PB) of the ROM. On the other hand, the discontinuous tiered transition is associated with multiple saddle-node (SN) bifurcations along with a supercritical PB and the first-order transition involves a subcritical PB alongside a SN bifurcation. Finally, the stability analysis of the different synchronization states of the system is performed analytically.
Complex network analysis of cryptocurrency market during crashes
Kundan Mukhia,Anish Rai,Luwang,Md Nurujjaman,Sushovan Majhi,Chittaranjan Hens
Physica A: Statistical Mechanics and its Applications, Physica-A, 2024
@inproceedings{bib_Comp_2024, AUTHOR = {Mukhia, Kundan and Rai, Anish and Luwang, and Nurujjaman, Md and Majhi, Sushovan and Hens, Chittaranjan }, TITLE = {Complex network analysis of cryptocurrency market during crashes}, BOOKTITLE = {Physica A: Statistical Mechanics and its Applications}. YEAR = {2024}}
This paper identifies the cryptocurrency market crashes and analyses its dynamics using the
complex network. We identify three distinct crashes during 2017–20, and the analysis is carried
out by dividing the time series into pre-crash, crash, and post-crash periods. Partial correlation
based complex network analysis is carried out to study the crashes. Degree density (𝜌𝐷), average
path length (̄𝑙), and average clustering coefficient (𝑐𝑐) are estimated from these networks. We
find that both 𝜌𝐷 and 𝑐𝑐 are smallest during the pre-crash period, and spike during the crash
suggesting the network is dense during a crash. Although 𝜌𝐷 and 𝑐𝑐 decrease in the postcrash
period, they remain higher than pre-crash levels for the 2017–18 and 2018–19 crashes
suggesting a market attempt to return to normalcy. We get ̄𝑙 is minimal during the crash period,
suggesting a rapid flow of information. A dense network and rapid information flow suggest
that during a crash uninformed synchronized panic sell-off happens. However, during the 2019–
20 crash, the values of 𝜌𝐷, 𝑐𝑐, and ̄𝑙 did not vary significantly, indicating minimal change in
dynamics compared to other crashes. The findings of this study may guide investors in making
decisions during market crashes.
Impact of local navigation rules on biased random walks in
multiplex Markov chains
Arpit Kumar,Subrata Ghosh,Pinaki Pal,Chittaranjan Hens
Physica A: Statistical Mechanics and its Applications, Physica-A, 2024
@inproceedings{bib_Impa_2024, AUTHOR = {Kumar, Arpit and Ghosh, Subrata and Pal, Pinaki and Hens, Chittaranjan }, TITLE = {Impact of local navigation rules on biased random walks in
multiplex Markov chains}, BOOKTITLE = {Physica A: Statistical Mechanics and its Applications}. YEAR = {2024}}
Our investigation centres on assessing the importance of a biased parameter (𝛼) in a multiplex
Markov chain (MMC) model that is characterized by biased random walks in multiplex networks.
We explore how varying complex network topologies affect the total multiplex imbalance
as a function of biased parameter. Our primary finding is that the system demonstrates a gradual
increase in total imbalance within both positive and negative regions of the biased parameter,
with a consistent minimum value occurring at 𝛼 = −1. In contrast to the negative region, the
total imbalance is consistently high when 𝛼 is significantly positive. We perform a detailed
examination of four different network structures and establish three sets of multiplex networks.
In each of these networks, the second layer consists of a Regular Random network, while the
first layer is either a Barabási–Albert, Erdős-Rényi, or Watts Strogatz network, depending on
the set. Our results demonstrate that the combination of Barabási–Albert and Random Regular
Network exhibits the highest level of right saturation imbalance. Additionally, for left saturation
imbalance, the Erdős–Rényi and Random Regular combination achieve a slightly higher value.
We also observe that the total amount of imbalance at 𝛼 = −1 follows a decreasing trend as
the size of the network of each layer increases. Furthermore, we are also able to illustrate that
the second most significant eigenvalue of the supra-transition matrix exhibits a similar pattern
in response to changes in the bias parameter, aligning with the overall system’s imbalance.
Symmetry invariance in nonlinear dynamical complex networks
Chittaranjan Hens
Chaos, Solitons & Fractals, CSF, 2024
Abs | | bib Tex
@inproceedings{bib_Symm_2024, AUTHOR = {Hens, Chittaranjan }, TITLE = {Symmetry invariance in nonlinear dynamical complex networks}, BOOKTITLE = {Chaos, Solitons & Fractals}. YEAR = {2024}}
We delve into the interplay between network’s symmetry and functioning for a generic class of dynamical
systems. Primarily, we focus on a class of systems that characterize the spreading process, such as the
spread of epidemics in complex networks, where the coupling configuration is nonlinear rather than diffusive.
Through theoretical and numerical analysis, we establish a compelling connection between the symmetry
of the graph and the trajectories followed by the dynamical processes for those nodes forming symmetry
orbits and displaying identical eigenvector centrality. In particular, we are able to show that when the initial
transitory states are removed, the symmetric group of nodes respond synchronously; nonetheless, they maintain
a constant distance from each other and hence follow splay states. We have verified this phenomenon once
more using two distinct kinds of networks. In one instance, every node takes part in nontrivial clusters. In the
alternative scenario, we create symmetric orbits as per our target. The cluster nodes show splay states in both
situations.
Complexity measure of extreme events
Dhiman Das,Arnob Ray,Chittaranjan Hens,Dibakar Ghosh,Md. Kamrul Hassan,Artur Dabrowski,Tomasz Kapitaniak,Syamal K. Dana
@inproceedings{bib_Comp_2024, AUTHOR = {Das, Dhiman and Ray, Arnob and Hens, Chittaranjan and Ghosh, Dibakar and Hassan, Md. Kamrul and Dabrowski, Artur and Kapitaniak, Tomasz and Dana, Syamal K. }, TITLE = {Complexity measure of extreme events}, BOOKTITLE = {Chaos}. YEAR = {2024}}
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in
the laboratory or in nature. The literature is already rich in the description of such measures using a variety of entropy
and disequilibrium measures, separately or in combination. Chaotic signal was given prime importance in such studies
while no such measure was proposed so far, how complex were the extreme events when compared to non-extreme
chaos. We address here this question of complexity in extreme events and investigate if we can distinguish them from
non-extreme chaotic signal. The normalized Shannon entropy in combination with disequlibrium is used for our study
and it is able to distinguish between extreme chaos and non-extreme chaos and moreover, it depicts the transition points
from periodic to extremes via Pomeau-Manneville intermittency and, from small amplitude to large amplitude chaos
and its transition to extremes via interior crisis. We report a general trend of complexity against a system parameter
that increases during a transition to extreme events, reaches a maximum, and then starts decreasing. We employ three
models, a nonautonomous Liénard system, 2-dimensional Ikeda map and a 6-dimensional coupled Hindmarh-Rose
system to validate our proposition
Impact of diffusion on synchronization pattern of epidemics in non-identical metapopulation networks.
Anika Roy,Ujjwal Shekhar,Aditi Bose,Subrata Ghosh,Santosh Nannuru,Syamal Kumar Dana,Chittaranjan Hens
@inproceedings{bib_Impa_2024, AUTHOR = {Roy, Anika and Shekhar, Ujjwal and Bose, Aditi and Ghosh, Subrata and Nannuru, Santosh and Dana, Syamal Kumar and Hens, Chittaranjan }, TITLE = {Impact of diffusion on synchronization pattern of epidemics in non-identical metapopulation networks.}, BOOKTITLE = {Chaos}. YEAR = {2024}}
In a prior study, a novel deterministic compartmental model known as the SEIHRK model was introduced, shedding light on the pivotal role of test kits as an intervention strategy for mitigating epidemics. Particularly in heterogeneous networks, it was empirically demonstrated that strategically distributing a limited number of test kits among nodes with higher degrees substantially diminishes the outbreak size. The network's dynamics were explored under varying values of infection rate. In this research, we expand upon these findings to investigate the influence of migration on infection dynamics within distinct communities of the network. Notably, we observe that nodes equipped with test kits and those without tend to segregate into two separate clusters when coupling strength is low, but beyond a critical threshold coupling coefficient, they coalesce into a unified cluster. Building on this clustering phenomenon, we develop a reduced equation model and rigorously validate its accuracy through comprehensive simulations. We show that this property is observed in both complete and random graphs.
High-frequency stock market order transitions during the US–China trade war 2018: A discrete-time Markov chain analysis
Chittaranjan Hens
@inproceedings{bib_High_2024, AUTHOR = {Hens, Chittaranjan }, TITLE = {High-frequency stock market order transitions during the US–China trade war 2018: A discrete-time Markov chain analysis}, BOOKTITLE = {Chaos}. YEAR = {2024}}
Statistical analysis of high-frequency stock market order transaction data is conducted to understand order transition dynamics. We employ a first-order time-homogeneous discrete-time Markov chain model to the sequence of orders of stocks belonging to six different sectors during the US–China trade war of 2018. The Markov property of the order sequence is validated by the Chi-square test. We estimate the transition probability matrix of the sequence using maximum likelihood estimation. From the heatmap of these matrices, we found the presence of active participation by different types of traders during high volatility days. On such days, these traders place limit orders primarily with the intention of deleting the majority of them to influence the market. These findings are supported by high stationary distribution and low mean recurrence values of add and delete orders. Further, we found similar spectral gap and entropy rate values, which indicates that similar trading strategies are employed on both high and low volatility days during the trade war. Among all the sectors considered in this study, we observe that there is a recurring pattern of full execution orders in the Finance & Banking sector. This shows that the banking stocks are resilient during the trade war. Hence, this study may be useful in understanding stock market order dynamics and devise trading strategies accordingly on high and low volatility days during extreme macroeconomic events.
Ecological resilience in a circular world: Mutation and extinction in five-species ecosystems
Ashley Wilson,Karthik Viswanathan,Sirshendu Bhattacharya,Chittaranjan Hens
Chaos, Solitons & Fractals, CSF, 2024
Abs | | bib Tex
@inproceedings{bib_Ecol_2024, AUTHOR = {Wilson, Ashley and Viswanathan, Karthik and Bhattacharya, Sirshendu and Hens, Chittaranjan }, TITLE = {Ecological resilience in a circular world: Mutation and extinction in five-species ecosystems}, BOOKTITLE = {Chaos, Solitons & Fractals}. YEAR = {2024}}
In an ecosystem comprising coexisting species, mutations frequently occur. These mutations can be induced by various factors such as errors in DNA replication and exposure to chemicals. They constitute an intrinsic element of species evolution. This study investigates the impact of mutations on ecosystems, employing Gillespie simulations and the formulation of the First-passage extinction problem to assess their effects and examine extinction events. Our findings suggest first-extinction time and state distribution in a system with mutation follows intriguing behavior which promotes co-existence. There also exists a depression in the state space post which mutation extends the first-extinction time. Moreover, a system devoid of mutation exhibits a discernible inclination towards probabilities that lean in the direction of an endangered state space.
Contrarian role of phase and phase velocity coupling in synchrony of second-order phase oscillators
,Arindam Mishra,Suman Saha,Subrata Ghosh, Syamal Kumar Dana,Chittaranjan Hens
Physical Review E, PRE, 2023
@inproceedings{bib_Cont_2023, AUTHOR = {, and Mishra, Arindam and Saha, Suman and Ghosh, Subrata and Dana, Syamal Kumar and Hens, Chittaranjan }, TITLE = {Contrarian role of phase and phase velocity coupling in synchrony of second-order phase oscillators}, BOOKTITLE = {Physical Review E}. YEAR = {2023}}
Positive phase coupling plays an attractive role in inducing in-phase synchrony in an ensemble of phase oscillators. Positive coupling involving both amplitude and phase continues to be attractive, leading to complete synchrony in identical oscillators (limit cycle or chaotic) or phase coherence in oscillators with heterogeneity of parameters. In contrast, purely positive phase velocity coupling may originate a repulsive effect on pendulumlike oscillators (with rotational motion) to bring them into a state of diametrically opposite phases or a splay state. Negative phase velocity coupling is necessary to induce synchrony or coherence in the general sense. The contrarian roles of phase coupling and phase velocity coupling on the synchrony of networks of second-order phase oscillators have been explored here. We explain our proposition using networks of two model systems, a second-order phase oscillator representing the pendulum or the superconducting Josephson junction dynamics, and a voltage-controlled oscillations in neurons model. Numerical as well as semianalytical approaches are used to confirm our result
Perfect synchronization in complex networks with higher-order interactions
Sangita Dutta,Prosenjit Kundu,Pitambar Khanra,Pinaki Pal,Chittaranjan Hens
Physical Review E, PRE, 2023
@inproceedings{bib_Perf_2023, AUTHOR = {Dutta, Sangita and Kundu, Prosenjit and Khanra, Pitambar and Pal, Pinaki and Hens, Chittaranjan }, TITLE = {Perfect synchronization in complex networks with higher-order interactions}, BOOKTITLE = {Physical Review E}. YEAR = {2023}}
Achieving perfect synchronization in a complex network, specially in the presence of higher-order interactions (HOIs) at a targeted point in the parameter space, is an interesting, yet challenging task. Here we present a theoretical framework to achieve the same under the paradigm of the Sakaguchi-Kuramoto (SK) model. We analytically derive a frequency set to achieve perfect synchrony at some desired point in a complex network of SK oscillators with higher-order interactions. Considering the SK model with HOIs on top of the scale-free, random, and small world networks, we perform extensive numerical simulations to verify the proposed theory. Numerical simulations show that the analytically derived frequency set not only provides stable perfect synchronization in the network at a desired point but also proves to be very effective in achieving a high level of synchronization around it compared to the other choices of frequency sets. The stability and the robustness of the perfect synchronization state of the system are determined using the low-dimensional reduction of the network and by introducing a Gaussian noise around the derived frequency set, respectively.
Endowing networks with desired symmetries and modular behavior
Khanra,SUSOBHAN GHOSH,D. Aleja,Chittaranjan Hens
Physical Review E, PRE, 2023
@inproceedings{bib_Endo_2023, AUTHOR = {Khanra, and GHOSH, SUSOBHAN and Aleja, D. and Hens, Chittaranjan }, TITLE = {Endowing networks with desired symmetries and modular behavior}, BOOKTITLE = {Physical Review E}. YEAR = {2023}}
Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of designing a desired set of clusters and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.
Response of a three-species cyclic ecosystem to a short-lived elevation of death rate
Chittaranjan Hens,Sourin Chatterjee,Syamal K. Dana
Scientific Reports, SR, 2023
@inproceedings{bib_Resp_2023, AUTHOR = {Hens, Chittaranjan and Chatterjee, Sourin and Dana, Syamal K. }, TITLE = {Response of a three-species cyclic ecosystem to a short-lived elevation of death rate}, BOOKTITLE = {Scientific Reports}. YEAR = {2023}}
A balanced ecosystem with coexisting constituent species is often perturbed by different natural events that persist only for a finite duration of time. What becomes important is whether, in the aftermath, the ecosystem recovers its balance or not. Here we study the fate of an ecosystem by monitoring the dynamics of a particular species that encounters a sudden increase in death rate. For exploration of the fate of the species, we use Monte-Carlo simulation on a three-species cyclic rock-paper-scissor model. The density of the affected (by perturbation) species is found to drop exponentially immediately after the pulse is applied. In spite of showing this exponential decay as a short-time behavior, there exists a region in parameter space where this species surprisingly remains as a single survivor, wiping out the other two which had not been directly affected by the perturbation. Numerical simulations using stochastic differential equations of the species give consistency to our results.
Pattern change of precipitation extremes in Bear Island
Arnob Ray,Tanujit Chakraborty,Athulya Radhakrishnan,Chittaranjan Hens,Syamal K Dana,Dibakar Ghosh,Nuncio Murukesh
Technical Report, arXiv, 2023
@inproceedings{bib_Patt_2023, AUTHOR = {Ray, Arnob and Chakraborty, Tanujit and Radhakrishnan, Athulya and Hens, Chittaranjan and Dana, Syamal K and Ghosh, Dibakar and Murukesh, Nuncio }, TITLE = {Pattern change of precipitation extremes in Bear Island}, BOOKTITLE = {Technical Report}. YEAR = {2023}}
Interlayer antisynchronization in degree-biased duplex networks
Sayantan Nag Chowdhury,Sarbendu Rakshit,Chittaranjan Hens,Dibakar Ghosh
Physical Review E, PRE, 2023
Abs | | bib Tex
@inproceedings{bib_Inte_2023, AUTHOR = {Chowdhury, Sayantan Nag and Rakshit, Sarbendu and Hens, Chittaranjan and Ghosh, Dibakar }, TITLE = {Interlayer antisynchronization in degree-biased duplex networks}, BOOKTITLE = {Physical Review E}. YEAR = {2023}}
With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.
Resetting-mediated navigation of an active Brownian searcher in a homogeneous topography
Gourab Kumar Sar, Arnob Ray,Chittaranjan Hens, Arnab Pal
Soft matter, SM, 2023
Abs | | bib Tex
@inproceedings{bib_Rese_2023, AUTHOR = {Sar, Gourab Kumar and Ray, Arnob and Hens, Chittaranjan and , Arnab Pal }, TITLE = {Resetting-mediated navigation of an active Brownian searcher in a homogeneous topography }, BOOKTITLE = {Soft matter}. YEAR = {2023}}
Designing navigation strategies for search-time optimization remains of interest in various interdisciplinary branches in science. Herein, we focus on active Brownian walkers in noisy and confined environments, which are mediated by one such autonomous strategy, namely stochastic resetting. As such, resetting stops the motion and compels the walkers to restart from the initial configuration intermittently. The resetting clock is operated externally without any influence from the searchers. In particular, the resetting coordinates are either quenched (fixed) or annealed (fluctuating) over the entire topography. Although the strategy relies upon simple governing laws of motion, it shows a significant ramification for the search-time statistics, in contrast to the search process conducted by the underlying reset-free dynamics. Using extensive numerical simulations, we show that the resetting-driven protocols enhance the performance of these active searchers. This, however, depends robustly on the inherent search-time fluctuations, measured by the coefficient of variation of the underlying reset-free process. We also explore the effects of different boundaries and rotational diffusion constants on the search-time fluctuations in the presence of resetting. Notably, for the annealed condition, resetting is always found to expedite the search process. These features, as well as their applicability to more general optimization problems from queuing systems, computer science and randomized numerical algorithms, to active living systems such as enzyme turnover and backtracking recovery of RNA polymerases in gene expression, make resetting-based strategies universally promising.
Dimension reduction in higher-order contagious phenomena
Subrata Ghosh,Pitambar Khanra , Prosenjit Kundu, Peng Ji, Dibakar Ghosh,Chittaranjan Hens
Chaos, Chaos, 2023
Abs | | bib Tex
@inproceedings{bib_Dime_2023, AUTHOR = {Ghosh, Subrata and , Pitambar Khanra and Kundu, Prosenjit and Ji, Peng and Ghosh, Dibakar and Hens, Chittaranjan }, TITLE = {Dimension reduction in higher-order contagious phenomena }, BOOKTITLE = {Chaos}. YEAR = {2023}}
We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N-dimensional susceptible-infected-susceptible dynamics in the presence of higher-order interactions. Utilizing this reduction process, we are able to capture the microscopic and macroscopic behavior of infectious networks. We find that the microscopic state of nodes (fraction of stable healthy individual of each node) inversely scales with their degree, and it becomes diminished due to the presence of higher-order interactions. In this case, we analytically obtain that the macroscopic state of the system (fraction of infectious or healthy population) undergoes abrupt transition. Additionally, we quantify the network’s resilience, i.e., how the topological changes affect the stable infected population. Finally, we provide an alternative framework of dimension reduction based on the spectral analysis of the network, which can identify the critical onset of the disease in the presence or absence of higher-order interactions. Both reduction methods can be extended for a large class of dynamical models.
Signal propagation in complex networks
Peng Ji,Jürgen,Jiachen Ye,Yu Mu,Wei Lin,Yang Tian,Chittaranjan Hens,Perc, Matjaž,Tang, Yang,Jie Sun
Physics Reports, Phy R, 2023
Abs | | bib Tex
@inproceedings{bib_Sign_2023, AUTHOR = {Ji, Peng and Jürgen, and Ye, Jiachen and Mu, Yu and Lin, Wei and Tian, Yang and Hens, Chittaranjan and Perc, and Matjaž, and Tang, and Yang, and Sun, Jie }, TITLE = {Signal propagation in complex networks}, BOOKTITLE = {Physics Reports}. YEAR = {2023}}
Signal propagation in complex networks drives epidemics, is responsible for information going viral, promotes trust and facilitates moral behavior in social groups, enables the development of misinformation detection algorithms, and it is the main pillar supporting the fascinating cognitive abilities of the brain, to name just some examples. The geometry of signal propagation is determined as much by the network topology as it is by the diverse forms of nonlinear interactions that may take place between the nodes. Advances are therefore often system dependent and have limited translational potential across domains. Given over two decades worth of research on the subject, the time is thus certainly ripe, indeed the need is urgent, for a comprehensive review of signal propagation in complex networks. We here first survey different models that determine the nature of interactions between the nodes, including epidemic models, Kuramoto models, diffusion models, cascading failure models, and models describing neuronal dynamics. Secondly, we cover different types of complex networks and their topologies, including temporal networks, multilayer networks, and neural networks. Next, we cover network time series analysis techniques that make use of signal propagation, including network correlation analysis, information transfer and nonlinear correlation tools, network reconstruction, source localization and link prediction, as well as approaches based on artificial intelligence. Lastly, we review applications in epidemiology, social dynamics, neuroscience, engineering, and robotics. Taken together, we thus provide the reader with an up-to-date review of the complexities associated with the network’s role in propagating signals in the hope of better harnessing this to devise innovative applications across engineering, the social and natural sciences as well as to inspire future research.
Emergent stability in complex network dynamics
Chandrakala Meena,Chittaranjan Hens,Suman Acharyya,Simcha Haber,Stefano Boccaletti,Baruch Barzel
Nature Physics, NP, 2023
Abs | | bib Tex
@inproceedings{bib_Emer_2023, AUTHOR = {Meena, Chandrakala and Hens, Chittaranjan and Acharyya, Suman and Haber, Simcha and Boccaletti, Stefano and Barzel, Baruch }, TITLE = {Emergent stability in complex network dynamics}, BOOKTITLE = {Nature Physics}. YEAR = {2023}}
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, real-world networks often appear random and highly irregular, raising the question of what are the naturally emerging organizing principles of complex system stability. The answer is encoded within the system’s stability matrix—the Jacobian—but is hard to retrieve, due to the scale and diversity of the relevant systems, their broad parameter space and their nonlinear interaction dynamics. Here we introduce the dynamic Jacobian ensemble, which allows us to systematically investigate the fixed-point dynamics of a range of relevant network-based models. Within this ensemble, we find that complex systems exhibit discrete stability classes
Detection and forecasting of extreme events in stock price triggered by fundamental, technical, and external factors
Anish Rai,Salam Rabindrajit Luwang,Md Nurujjaman,Chittaranjan Hens,Pratyay Kuila,Kanish Debnath
Chaos, Solitons & Fractals, CSF, 2023
Abs | | bib Tex
@inproceedings{bib_Dete_2023, AUTHOR = {Rai, Anish and Luwang, Salam Rabindrajit and Nurujjaman, Md and Hens, Chittaranjan and Kuila, Pratyay and Debnath, Kanish }, TITLE = {Detection and forecasting of extreme events in stock price triggered by fundamental, technical, and external factors}, BOOKTITLE = {Chaos, Solitons & Fractals}. YEAR = {2023}}
The sporadic large fluctuations seen in the stock market are due to different factors. These large fluctuations are termed extreme events (EE). We have identified fundamental, technical, and external factors and categorized positive or negative EE depending on the impact of these factors. During such events, the stock price time series is found to be nonstationary. Hence, the Hilbert–Huang transformation is used to identify EEs based on high instantaneous energy () concentration. The analysis shows that concentration in the stock price is very high during both positive and negative EE, surpassing a threshold of where and are the mean energy and standard deviation of energy, respectively. Further, support vector regression is used to predict the stock price during an EE, with the close price being found to be the most useful input than the open-high-low-close (OHLC) inputs. The maximum prediction accuracy for one step using close price and OHLC prices are 95.98% and 95.64%, respectively. Whereas, for the two step prediction, the accuracies are 94.09% and 93.58%, respectively. These results highlight that the accuracy of one-step predictions surpasses that of two-step predictions. Also, accuracy decreases when predicting stock prices closer to an EE. The EEs identified from predicted time series exhibit statistical characteristics similar to those obtained from the original data.
Predicting aging transition using Echo state network
Biswambhar Rakshit, Aryalakshmi S, Arjun J. Kartha,Chittaranjan Hens
Chaos, Chaos, 2023
Abs | | bib Tex
@inproceedings{bib_Pred_2023, AUTHOR = {Rakshit, Biswambhar and S, Aryalakshmi and Kartha, Arjun J. and Hens, Chittaranjan }, TITLE = {Predicting aging transition using Echo state network}, BOOKTITLE = {Chaos}. YEAR = {2023}}
It is generally known that in a mixture of coupled active and inactive nonlinear oscillators, the entire system may stop oscillating and become inactive if the fraction of active oscillators is reduced to a critical value. This emerging phenomenon, called the “aging transition,” can be analytically predicted from the view point of cluster synchronization. One can question whether a model-free, data-driven framework based on neural networks could be used to foretell when such a system will cease oscillation. Here, we demonstrate how a straightforward ESN with trained output weights can accurately forecast both the temporal evaluation and the onset of collapse in coupled paradigmatic limit-cycle oscillators. In particular, we have demonstrated that an ESN can identify the critical fraction of inactive oscillators in a large all-to-all, small-world, and scale-free network when it is trained only with two nodes (one active and the other inactive) selected from three different pre-collapse regimes. We further demonstrate that ESN can anticipate aging transition of the network when trained with the mean-field dynamics of active and inactive oscillators.
Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems
Sanjeev K. Sharma,Argha Mondal,Eva Kaslik,Chittaranjan Hens,Chris G. Antonopoulos
Scientific Reports, SR, 2023
@inproceedings{bib_Dive_2023, AUTHOR = {Sharma, Sanjeev K. and Mondal, Argha and Kaslik, Eva and Hens, Chittaranjan and Antonopoulos, Chris G. }, TITLE = {Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems}, BOOKTITLE = {Scientific Reports}. YEAR = {2023}}
The diverse excitabilities of cells often produce various spiking‑bursting oscillations that are found in the neural system. We establish the ability of a fractional‑order excitable neuron model with Caputo’s fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris‑Lecar (M‑L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional‑order neuron. We then extend the study with the 3D slow‑fast M‑L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional‑order and classical integer‑order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös‑Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced‑order model which can capture the activities of the entire network. Our results reveal that the effect of fractional‑order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.
Predicting the data structure prior to extreme events from passive observables using Echo State network
Abhirup Banerjee,Arindam Mishra,Syamal Kumar Dana,Chittaranjan Hens,Tomasz Kapitaniak,Jürgen Kurths,Norbert Marwan
Frontiers in Applied Mathematics and Statistics, FAMS, 2022
@inproceedings{bib_Pred_2022, AUTHOR = {Banerjee, Abhirup and Mishra, Arindam and Dana, Syamal Kumar and Hens, Chittaranjan and Kapitaniak, Tomasz and Kurths, Jürgen and Marwan, Norbert }, TITLE = {Predicting the data structure prior to extreme events from passive observables using Echo State network}, BOOKTITLE = {Frontiers in Applied Mathematics and Statistics}. YEAR = {2022}}
Extreme events are defined as events that largely deviate from the nominal state of the system as observed in a time series. Due to the rarity and uncertainty of their occurrence, predicting extreme events has been challenging. In real life, some variables (passive variables) often encode significant information about the occurrence of extreme events manifested in another variable (active variable). For example, observables such as temperature, pressure, etc., act as passive variables in case of extreme precipitation events. These passive variables do not show any large excursion from the nominal condition yet carry the fingerprint of the extreme events. In this study, we propose a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable that leads to an extreme event using information from the passive variable. An appropriate threshold height of events is a prerequisite for detecting extreme events and improving the skill of their prediction. We demonstrate that the magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series aect the prediction skill. Quantitatively, we confirm this using a metric describing the mean phase dierence between the input time signals, which decreases when the magnitude of the extreme event is relatively higher, thereby increasing the predictability skill
Model-free prediction of multistability using echo state network
Mousumi Roy, Swarnendu Mandal,Chittaranjan Hens,Awadhesh Prasad,N.V. Kuznetsov,Manish Dev Shrimali
@inproceedings{bib_Mode_2022, AUTHOR = {Roy, Mousumi and Mandal, Swarnendu and Hens, Chittaranjan and Prasad, Awadhesh and Kuznetsov, N.V. and Shrimali, Manish Dev }, TITLE = {Model-free prediction of multistability using echo state network}, BOOKTITLE = {Chaos}. YEAR = {2022}}
In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse systems ranging from climate to finance, ecological to social systems. In this article, we investigate a data-driven approach to infer different dynamics of a multistable system using echo state network (ESN). We start with a parameter-aware reservoir and predict diverse dynamics for different parameter values. Interestingly, machine is able to reproduce the dynamics almost perfectly even at distant parameters which lie considerably far from the parameter values related to the training dynamics. In continuation, we can predict whole bifurcation diagram significant accuracy as well. We extend this study for exploring various dynamics of multistable attractors at unknown parameter value. While, we train the machine with the dynamics of only one attarctor at parameter p, it can capture the dynamics of co-existing attractor at a new parameter value p+∆p. Continuing the simulation for multiple set of initial conditions, we can identify the basins for different attractors. We generalize the results by applying the scheme on two distinct multistable systems.
Extreme events in a complex network: Interplay between degree distribution and repulsive interaction
Arnob Ray,Timo Bröhl,Arindam Mishra,Subrata Ghosh,Dibakar Ghosh,Tomasz Kapitaniak,Syamal K Dana,Chittaranjan Hens
Chaos, Chaos, 2022
Abs | | bib Tex
@inproceedings{bib_Extr_2022, AUTHOR = {Ray, Arnob and Bröhl, Timo and Mishra, Arindam and Ghosh, Subrata and Ghosh, Dibakar and Kapitaniak, Tomasz and Dana, Syamal K and Hens, Chittaranjan }, TITLE = {Extreme events in a complex network: Interplay between degree distribution and repulsive interaction}, BOOKTITLE = {Chaos}. YEAR = {2022}}
The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-field repulsive interactions. An interplay of topological heterogeneity and the repulsive interaction between the dynamical units of the network triggers extreme events in the nodes when each node succumbs to such events for discretely different ranges of repulsive coupling. A high degree node is vulnerable to weaker repulsive interactions, while a low degree node is susceptible to stronger interactions. As a result, the formation of extreme events changes position with increasing strength of repulsive interaction from high to low degree nodes. Extreme events at any node are identified with the appearance of occasional large-amplitude events (amplitude of the temporal dynamics) that are larger than a threshold height and rare in occurrence, which we confirm by estimating the probability distribution of all events. Extreme events appear at any oscillator near the boundary of transition from rotation to libration at a critical value of the repulsive coupling strength. To explore the phenomenon, a paradigmatic second-order phase model is used to represent the dynamics of the oscillator associated with each node. We make an annealed network approximation to reduce our original model and, thereby, confirm the dual role of the repulsive interaction and the degree of a node in the origin of extreme events in any oscillator associated with a node. ACKNOWLEDGMENTS
Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions
Sourin Chatterjee,Sayantan Nag Chowdhury,Dibakar Ghosh,Chittaranjan Hens
Journal of Nonlinear Science, choas, 2022
@inproceedings{bib_Cont_2022, AUTHOR = {Chatterjee, Sourin and Chowdhury, Sayantan Nag and Ghosh, Dibakar and Hens, Chittaranjan }, TITLE = {Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions}, BOOKTITLE = {Journal of Nonlinear Science}. YEAR = {2022}}
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel perspective for understanding the influence of higher-order interactions on the evolution of social phenotypes. Our simple model yields a prosperous outlook to demonstrate the impact of perturbations on intransitive competitive higherorder interactions. Using a mathematical technique, we show how alone the perturbed interaction network can quickly determine the coexistence equilibrium of competing species instead of solving a large system of ordinary differential equations. It is possible to split the system into multiple feasible cluster states depending on the number of perturbations. Our analysis also reveals the ratio between the unperturbed and perturbed species is inversely proportional to the amount of employed perturbation. Our results suggest that nonlinear dynamical systems and interaction topologies can be interplayed to comprehend species’ coexistence under adverse conditions. Particularly our findings signify that less competition between two species increases their abundance and outperforms others
