Related papers: A type of shadowing and distributional chaos
We consider Rayleigh particles in a periodically modulated optical trap formed by two counter-propagating Gaussian beams. It is shown that for certain values of parameters the system exhibits transient chaos which manifests itself in…
The concept of A-coupled-expanding map, which is one of the more natural and useful ideas generalized the horseshoe map, is well known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.
We consider the classical map proposed previously to be the exact classical analogue of Rydberg Molecules calculated with the approximations relevant to the multi-channel quantum defect theory. The resulting classical map is analyzed at…
The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…
On long enough timescales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The solar system is no exception: diffusive processes take part in the transportation of small bodies and provide…
We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…
In this paper, we introduce several new types and generalizations of the concepts distributional chaos and Li-Yorke chaos. We consider the general sequences of binary relations acting between metric spaces, while in a separate section we…
The main aim of the present paper is to study relations between $n$-scrambled tuples and their attraction-adherence properties with respect to various sequences of integers. This extends previous research on relations between chaos in the…
We review recent progress in applying information- and computation-theoretic measures to describe material structure that transcends previous methods based on exact geometric symmetries. We discuss the necessary theoretical background for…
When a medium composed of microscopic elements is subjected to a high intensity field, the individual behaviors of microscopic elements can become chaotic. In such cases it is important to consider the effects of this irregularity at…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…
Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by Random Matrix Theory. Scattering resonances…
We consider the logistic equation with different types of the piecewise constant argument. It is proved that the equation generates chaos and intermittency. Li-Yorke chaos is obtained as well as the chaos through period-doubling route.…
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
Motivated by three recent open questions in the study of linear dynamics, we study weighted shifts on sequence spaces. First, we provide an example of a weighted shift on a locally convex space whose topology is generated by a sequence of…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…