Spatial locking of chimera states to frequency heterogeneity in nonlocally coupled oscillators

TL;DR

This paper investigates how frequency heterogeneity in nonlocally coupled oscillators causes spatial locking of chimera states, aligning coherent and incoherent regions with specific frequency zones, and provides a theoretical framework for understanding this phenomenon.

Contribution

It introduces the concept of spatial locking of chimera states induced by frequency heterogeneity and develops a self-consistency approach and variational analysis to explain this behavior.

Findings

Frequency heterogeneity induces spatial locking of chimera states.

Steady solutions of the continuum system reproduce locked chimera states.

The variational argument explains the mechanism behind spatial locking.

Abstract

Chimera states in systems of nonlocally coupled oscillators, i.e., self-organized coexistence of coherent and incoherent oscillator populations, have attracted much attention. In this study, we consider the effect of frequency heterogeneities on the chimera state and reveal that it induces spatial locking of the chimera state, i.e., the coherent and incoherent domains align with lower and higher frequency regions, respectively, in a self-adaptive manner. Using an extended self-consistency approach, we show that such spatially locked chimera states can be reproduced as steady solutions of the system in the continuum limit. Furthermore, we develop a variational argument to explain the mechanism leading to spatial locking. Our analysis reveals how heterogeneity can affect the collective dynamics of the chimera states and offers insights into their control and applications.