Related papers: Testing for Chaos in Deterministic Systems with No…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
This paper introduces a novel parameterization to characterize unknown linear time-invariant systems using noisy data. The presented parameterization describes exactly the set of all systems consistent with the available data. We then…
We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies…
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…
In this article, we review our recently introduced methods for obtaining strictly positive lower bounds on the top Lyapunov exponent of high-dimensional, stochastic differential equations such as the weakly-damped Lorenz-96 (L96) model or…
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 explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by…
Identifying and suppressing unknown disturbances to dynamical systems is a problem with applications in many different fields. Here we present a model-free method to identify and suppress an unknown disturbance to an unknown system based…
This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed…
In this paper, we investigate the mean-square stabilization for discrete-time stochastic systems that endure both multiple input delays and multiplicative control-dependent noises. For such multi-delay stochastic systems, we for the first…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
Understanding and quantifying chaos from data remains challenging. We present a data-driven method for estimating the largest Lyapunov exponent (LLE) from one-dimensional chaotic time series using machine learning. A predictor is trained to…
A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using $k$-digits to the right from the decimal separator of a…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We define a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure, thanks to the addition of infinitesimal noise. The zero-noise limit can be handled by…
A recently proposed test for chaos [Gottwald G A and Melbourne I 2004 \textit{Proc. R. Soc. London A} {\bf 460} 603-611] is employed to probe the Hamiltonian dynamics of a one-dimensional anharmonic oscillator lattice. For a homogeneous…