Chimera states in hierarchical networks of Van der Pol oscillators

TL;DR

This paper explores how hierarchical coupling topologies influence the emergence and characteristics of chimera states in networks of Van der Pol oscillators, revealing the role of clustering coefficient and amplitude dynamics.

Contribution

It introduces the network clustering coefficient as a key measure linking hierarchical topology to chimera state occurrence and analyzes the effects of hierarchy and base pattern on chimera diversity.

Findings

Large clustering coefficient promotes chimera states.

Different base patterns lead to various incoherent domain counts.

Amplitude dynamics become more prominent in larger networks.

Abstract

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in networks of Van der Pol oscillators with hierarchical coupling topology. We investigate the stepwise transition from a nonlocal to a hierarchical topology, and propose the network clustering coefficient as a measure to establish a link between the existence of chimera states and the compactness of the initial base pattern of a hierarchical topology; we show that a large clustering coefficient promotes the occurrence of chimeras. Depending on the level of hierarchy and base pattern, we obtain chimera states with different numbers of incoherent domains. We investigate the chimera regimes as a function of coupling strength and nonlinearity parameter of the individual oscillators. The analysis of a network with larger base pattern resulting in larger clustering coefficient reveals two different types of chimera states and highlights the increasing role of amplitude dynamics.