Chimera states in systems of nonlocal nonidentical phase-coupled oscillators

TL;DR

This paper investigates how spatial inhomogeneity affects the formation, stability, and properties of chimera states in nonlocally coupled phase oscillators, revealing mechanisms like pinning and trapping.

Contribution

It introduces a detailed analysis of localized and periodic inhomogeneities' effects on chimera states, including the development of an evolution equation for the complex order parameter.

Findings

Inhomogeneity breaks splay states.

It pins chimera states to specific locations.

It traps traveling chimeras.

Abstract

Chimera states consisting of domains of coherently and incoherently oscillating nonlocally-coupled phase oscillators in systems with spatial inhomogeneity are studied. The inhomogeneity is introduced through the dependence of the oscillator frequency on its location. Two types of spatial inhomogeneity, localized and spatially periodic, are considered and their effects on the existence and properties of multi-cluster and traveling chimera states are explored. The inhomogeneity is found to break up splay states, to pin the chimera states to specific locations and to trap traveling chimeras. Many of these states can be studied by constructing an evolution equation for a complex order parameter. Solutions of this equation are in good agreement with the results of numerical simulations.