Related papers: Generic and dense distributional chaos with shadow…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…
Understanding the far-from-equilibrium dynamics of dissipative quantum systems, where dissipation and decoherence coexist with unitary dynamics, is an enormous challenge with immense rewards. Often, the only realistic approach is to forgo a…
We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular…
While classical chaos is defined via a system's sensitive dependence on its initial conditions (SDIC), this notion does not directly extend to quantum systems. Instead, recent works have established defining both quantum and classical chaos…
A precise definition of chaos for discrete processes based on iteration already exists. We shall first reformulate it in a more general frame, taking into account the fact that discrete chaotic behavior is neither necessarily based on…
In this paper we study relations between almost specification property, asymptotic average shadowing property and average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and…
We present an analysis of chaos and regularity in the open Dicke model, when dissipation is due to cavity losses. Due to the infinite Liouville space of this model, we also introduce a criterion to numerically find a complex spectrum which…
In this paper we solve two open problems concerning distributional chaos in non-autonomous discrete dynamical systems stated in [4] and [17]. In the first problem it is wondered if the limit function of pointwise convergent non-autonomous…
We introduce several different notions of disjoint distributional chaos for sequences of multivalued linear operators in Fr\'echet spaces. Any of these notions seems to be new and not considered elsewhere even for linear continuous…
We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters.…
In this paper, we discuss the relationship between Li-Yorke chaos and distributional chaos in a sequence. We point out the set of all distributional $\delta$-scramble pairs in the sequence $Q$ is a $G_\delta$ set, and prove that Li-Yorke…
Using standard definitions of chaos (as positive Kolmogorov-Sinai entropy) and diffusion (that multiple time distribution functions are Gaussian), we show numerically that both chaotic and nonchaotic systems exhibit diffusion, and hence…
Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling betweenthe systems are analyzed. The…
In the present paper, an essential generalization of the symbolic dynamics is considered. We apply the notions of abstract self-similar sets and the similarity map for a chaos introduction, which orbits are expanded among infinitely many…
This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the…
Using a combination of analytical and numerical techniques, we show that chaos in globally-coupled identical dynamical systems, be they dissipative or Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov exponents is…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…