Related papers: Topological chaos: what may this mean ?
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
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…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
The notion of primitive chaos was proposed [J. Phys. Soc. Jpn. {\bf 79}, 15002 (2010)] as a notion closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility.…
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…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
We discuss how the concept of the quantum action can be used to characterize quantum chaos. As an example we study quantum mechanics of the inverse square potential in order to test some questions related to quantum action. Quantum chaos is…
We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
In this paper, we study various chaos of topological group or semigroup actions.
Topological effects produce chaos in multiagent simulation and distributed computation. We explain this result by developing three themes concerning complex systems in the natural and social sciences: (i) Pragmatically, a system is complex…
We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos…
Based on newly discovered properties of the shift map (Theorem 1), we believe that chaos should involve not only nearby points can diverge apart but also faraway points can get close to each other. Therefore, we propose to call a continuous…
We shortly review the progress in the domain of deterministic chaos for quantum dynamical systems. With the appropriately extended definition of quantum Lyapunov exponent we analyze various quantum dynamical maps. It is argued that, within…
New features related to collective properties generated in the systems driven by random dynamics are observed and their implications for further understanding of interplay between coherence and chaos are discussed.