Sporadicity and synchronization in one-dimensional asymmetrically coupled maps

TL;DR

This paper investigates how asymmetry in coupling affects synchronization and chaos in a one-dimensional chain of sporadic maps, revealing a transition from full synchronization to chaos as asymmetry varies.

Contribution

It introduces a numerical study of asymmetric couplings in one-dimensional sporadic maps, showing how asymmetry influences synchronization and chaos.

Findings

Strong asymmetry leads to full spatial synchronization with zero Lyapunov exponent.

Weak asymmetry results in partial synchronization and positive Lyapunov exponent.

A direct relation exists between temporal chaos and spatial synchronization.

Abstract

A one-dimensional chain of sporadic maps with asymmetric nearest neighbour couplings is numerically studied. It is shown that in the region of strong asymmetry the system becomes spatially fully synchronized, even in the thermodinamic limit, while the Lyapunov exponent is zero. For weak asymmetry the synchronization is no more complete, and the Lyapunov exponent becomes positive. In addition one has a clear relation between temporal and spatial chaos, {\it i.e.}: a positive effective Lyapunov exponent corresponds to a lack of synchronization and {\it vice versa}