Chimera-like behavior in a heterogeneous Kuramoto model: the interplay between the attractive and repulsive coupling

TL;DR

This paper investigates how heterogeneous interactions in a Kuramoto oscillator network lead to a unique chimera-like state during synchronization transitions, influenced by network topology and coupling types.

Contribution

It reveals the emergence of a frequency-modulated chimera-like pattern caused by the interplay of attractive and repulsive couplings in heterogeneous networks.

Findings

Chimera-like states occur during explosive synchronization transitions.

Network topology significantly affects the emergence of chimera-like patterns.

Weakly non-local and small-world networks support the chimera-like behavior.

Abstract

Interaction within an ensemble of coupled nonlinear oscillators induces a variety of collective behaviors. One of the most fascinating is a chimera state which manifests the coexistence of spatially distinct populations of coherent and incoherent elements. Understanding of the emergent chimera behavior in controlled experiments or real systems requires a focus on the consideration of heterogeneous network models. In this study, we explore the transitions in a heterogeneous Kuramoto model under the monotonical increase of the coupling strength and specifically find that this system exhibits a frequency-modulated chimera-like pattern during the explosive transition to synchronization. We demonstrate that this specific dynamical regime originates from the interplay between (the evolved) attractively and repulsively coupled subpopulations. We also show that the above mentioned chimera-like state is induced under weakly non-local, small-world and sparse scale-free coupling and suppressed in globally coupled, strongly rewired and dense scale-free networks due to the emergence of the large-scale connections.