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How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent…

There are lots of results to study dynamical complexity on irregular sets and level sets of ergodic average from the perspective of density in base space, Hausdorff dimension, Lebesgue positive measure, positive or full topological entropy…

Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…

Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…

We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…

In this work, the topologies of networks constructed from time series from an underlying system undergo a period doubling cascade have been explored by means of the prevalence of different motifs using an efficient computational motif…

We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development…

This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…

We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…

We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…

We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…

The method of reconstruction of an attractor from a set of short time series ({\it clusters}) is proposed and discussed. This method is most useful for correlation dimension estimation of experimental data.

This paper presents an automated machine learning framework designed to assist hydrologists in detecting anomalies in time series data generated by sensors in a research watershed in the northeastern United States critical zone. The…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between…

Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a…

We analyze the statistical complexity vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period {\tau}. It is shown that if the Bandt and Pompe procedure is used to assign a probability distribution…

Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network…