Related papers: Chaos on compact metric spaces generated from symb…
This work theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For…
This talk summarises what is currently understood about the phenomenon that has come to be known as {\it chaotic mixing}. The first part presents a concise statement as to what chaotic mixing actually is, and then explains why it should be…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
There exists a compact manifold so that the set of topologically chaotic but statistically trivial $C^{r} (1\leq r \leq \infty)$ vector fields on this manifold displays considerable scale in the view of dimension. More specifically, it…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
A novel type of self-organized lattice in which chaotic defects are arranged periodically is reported for a coupled map model of open flow. We find that temporally chaotic defects are followed by spatial relaxation to an almost periodic…
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…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output reinjected after a certain delay. For a class of simple maps, we give analytic conditions for the…
In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based…
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
We introduce pointwise measure expansivity for bi-measurable maps. We show through examples that this notion is weaker than measure expansivity. In spite of this fact, we show that many results for measure expansive systems hold true for…
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…
We introduce two parametrized families of piecewise affine maps on $[0,1]^2$ and $[0,1]^3$, as generalizations of the heterochaos baker maps which were introduced and investigated in [Y. Saiki, H. Takahasi, J. A. Yorke, Nonlinearity, 34…
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…
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…