Role of delay in the mechanism of cluster formation

TL;DR

This paper investigates how delay influences cluster formation in coupled maps, revealing that delay can alter interaction mechanisms and lead to diverse cluster patterns, with implications for understanding synchronization phenomena.

Contribution

It demonstrates that delay can fundamentally change the mechanism of cluster formation and synchronization in coupled maps, providing new insights into delay-induced dynamics.

Findings

Delay affects the mechanism of unit interactions.

Same parity delays produce similar cluster phenomena.

Delay can create new, rich cluster patterns.

Abstract

We study the role of delay in phase synchronization and phenomena responsible for cluster formation in delayed coupled maps on various networks. Using numerical simulations, we demonstrate that the presence of delay may change the mechanism of unit to unit interaction. At weak coupling values, same parity delays are associated with the same phenomenon of cluster formation and exhibit similar dynamical evolution. Intermediate coupling values yield rich delay-induced driven cluster patterns. A Lyapunov function analysis sheds light on the robustness of the driven clusters observed for delayed bipartite networks. Our results reveal that delay may lead to a completely different relation, between dynamical and structural clusters, than observed for the undelayed case.