Very long transients in globally coupled maps

TL;DR

This paper investigates the occurrence of very long transient behaviors in globally coupled logistic maps, showing how these transients lead to synchronized clusters and are affected by weak noise.

Contribution

It reveals the presence of long transients in a specific phase of coupled maps and analyzes the influence of noise on cluster stability and dynamics.

Findings

Long transients lead to synchronized cluster states.

Weak noise favors more stable periodic cluster configurations.

Transient behavior persists despite weak noise influence.

Abstract

Very long transients are found in the partially ordered phase of type II of globally coupled logistic maps. The transients always lead the system in this phase to a state with a few synchronous clusters. This transient behaviour is not significantly influenced by the introduction of weak noises. However, such noises generally favor cluster partitions with more stable periodic dynamics.