One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures

One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures.

Weak Synchronization of Chaotic Coupled Map Lattices

Phase synchronized states can emerge in the collective behavior of an ensemble of chaotic coupled map lattices, due to a mean field interaction. This type of interaction is responsible for synchronized chaotic global activity of the lattices, while the local activity of each map remains unsynchronized. The resulting collective dynamics is called “weak synchronization.” The transition to such a ...

Chaotic Synchronization in Coupled Map Lattices with Periodic Boundary Conditions

In this paper, we consider a lattice of the coupled logistic map with periodic boundary conditions. We prove that synchronization occurs in the one-dimensional lattice with lattice size n = 4 for any γ in the chaotic regime [γ∞ ≈ 3.57, 4]. It is worthwhile to emphasize that, despite of the fact that there is a rigorous proof for synchronization in many systems with continuous time, almost nothi...

GENERAL SYNCHRONIZATION OF COUPLED PAIR OF CHAOTIC ONE-DIMENSIONAL GAUSSIAN MAPS

In this paper we review some recent ideas of synchronization theory. We apply this theory to study the different synchronization aspects of uni-directionally coupled pair of chaotic one-dimensional Gaussian maps.

Bifurcations of Chaotic Attractors in One-Dimensional Piecewise Smooth Maps

It is well known that dynamical systems defined by piecewise smooth functions exhibit several phenomena which cannot occur in smooth systems, such as for example, border collision bifurcations, sliding, chattering, etc. [di Bernardo et al., 2008]. One such phenomenon is the persistence of chaotic attractors under parameter perturbations, referred to as robust chaos [Banerjee et al., 1998]. In t...