Abstract

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.

Abstract

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.

Abstract

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.

Abstract

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.

Abstract

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.

Abstract

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.

Abstract

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

Abstract

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.

Abstract

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.

Abstract

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.