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In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we provide a…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE)…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
In many physical systems, dynamics is ruled by structures of atypical chaoticity. These structures may occupy a very small volume in phase space and can thus be very difficult to locate numerically. In this article, we review an algorithm,…
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach…
We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment…
Proper states' representations are the key to the successful dynamics modeling of chaotic systems. Inspired by recent advances of deep representations in various areas such as natural language processing and computer vision, we propose the…
We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for dynamical systems, as well as of the numerical techniques developed for the computation of the maximal, of few and of all of them. After some historical…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
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…
As cities around the world aim to improve walkability and safety, understanding the irregular and unpredictable nature of pedestrian behavior has become increasingly important. This study introduces a data-driven framework for modeling…
in the last decade, studies of chaotic system are more often used for classical choatic system than for quantum chaotic system, there are many ways of observing the chaotic system such us analyzing the frequency with Fourier transform or…