Related papers: Genericity of distributional chaos in non-autonomo…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
For discrete autonomous dynamical systems (ADS) $(X, d, f)$, it was found that in the three conditions defining Devaney chaos, topological transitivity and dense periodic points together imply sensitive dependence on initial…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
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 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…
In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group G, we introduce local weak mixing and Li-Yorke chaos; and…
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of…
The problem of open-loop dynamical control of generic open quantum systems is addressed. In particular, I focus on the task of effectively switching off environmental couplings responsible for unwanted decoherence and dissipation effects.…
This paper discusses the thermodynamic properties for certain time-dependent dynamical systems. In particular, we are interested in time-dependent dynamical systems with the specification property. We show that each time-dependent dynamical…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of light chaos is the most significant. Severalexamples, which clarify the relationships between this kind of chaos and…
This paper considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different…
Impulsive control is used to suppress the chaotic behavior in an one-dimensional discrete supply and demand dynamical system. By perturbing periodically the state variable with constant impulses, the chaos can be suppressed. It is proved…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A Central Limit Theorem (CLT) is only…
We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…