Related papers: Analyzing Topological Mixing and Chaos on Continua…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical…
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L.…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as `weather regimes', loosely categorised as regions of phase space with above-average density and/or extended persistence. Their…
Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
The topological pressure introduced by Ruelle and similar quantities describe dynamical multifractal properties of dynamical systems. These are important characteristics of mesoscopic systems in the classical regime. Original definition of…
By using the reduction technique to impulsive differential equations [1], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos.…
We study discontinuous interval maps generated by the action of erasing block substitutions on the binary expansion. After establishing some general properties of these maps, we categorize erasing block substitutions in a hierarchy of…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
In the scope of the statistical description of dynamical systems, one of the defining features of chaos is the tendency of a system to lose memory of its initial conditions (more precisely, of the distribution of its initial conditions).…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
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 investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…
We define new isomorphism-invariants for ergodic measure-preserving systems on standard probability spaces, called measure-theoretic chaos and measure-theoretic$^+$ chaos. These notions are analogs of the topological chaoses {\rm DC2} and…