Impact of leader on cluster synchronization

TL;DR

This paper investigates how introducing a leader node affects cluster synchronization in coupled oscillators, revealing transitions in cluster patterns and formation mechanisms influenced by frequency mismatch and system dynamics.

Contribution

It demonstrates that a leader induces significant changes in cluster formation and mechanisms, highlighting the role of frequency mismatch and system dynamics in synchronization.

Findings

Leader presence alters cluster patterns and formation mechanisms.

Frequency mismatch drives the transition from driven to mixed clusters.

Chaotic systems primarily use driven mechanisms, while periodic systems also involve self-organization.

Abstract

We study the mechanisms of frequency synchronized cluster formation in coupled non-identical oscillators and investigate the impact of presence of a leader on the cluster synchronization. We find that the introduction of a leader, node having large parameter mismatch, induces a profound change in the cluster pattern as well as in the mechanism of the cluster formation. The emergence of a leader generates a transition from the driven to the mixed cluster state. The frequency mismatch turns out to be responsible for this transition. Additionally, for a chaotic evolution, the driven mechanism stands as a primary mechanism for the cluster formation, whereas for a periodic evolution the self-organization mechanism becomes equally responsible.