Sporadicity and synchronization in one-dimensional asymmetrically coupled maps

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.

Global Analysis of Synchronization in Coupled Maps

We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two symmetrically coupled tent maps, we also treat the case of two asymmetrically coupled tent maps as well as a globally coupled network. Our main result is the identifica...

Synchronization in Ensembles of Coupled Maps with a Major Element

The paper investigates the conditions for full and partial synchronization in systems of coupled chaotic maps that include the presence of a major element, that is, an element that interacts with all the other elements of the system. We consider a system which consists of two globally coupled populations of one-dimensional maps that interact via a major element. The presence of this element can...

ar X iv : c on d - m at / 9 30 50 01 v 1 3 M ay 1 99 3 One - dimensional asymmetrically coupled maps with defects

Modeling of spiking-bursting neural behavior using two-dimensional map.

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map that contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps that model th...