Locking and regularisation of chimeras by periodic forcing

TL;DR

This paper investigates how periodic external forcing influences chimera states in non-locally coupled oscillators, leading to frequency entrainment, pattern regularization, and complex locking behaviors across different dynamical levels.

Contribution

It provides a multi-level analysis of chimera responses to forcing, revealing new mechanisms of locking and regularization not previously characterized.

Findings

Chimera frequency can be entrained within an Arnold tongue.

Strong forcing regularizes unstationary chimera patterns.

Forcing outside the Arnold tongue induces multi-plateau locking states.

Abstract

We study how a chimera state in a one-dimensional medium of non-locally coupled oscillators responses to a periodic external force. On a macroscopic level, where chimera can be considered as an oscillating object, forcing leads to entrainment of the chimera's frequency inside an Arnold tongue. On a mesoscopic level, where chimera can be viewed as a inhomogeneous, stationary or nonstationary pattern, strong forcing can lead to reguralization of an unstationary chimera. On a microscopic level of the dynamics of individual oscillators, forcing outside of the Arnold tongue leads to a multi-plateu state with nontrivial locking properties.