Dynamics and stability of chimera states in two coupled populations of oscillators

TL;DR

This paper investigates the dynamics and stability of chimera states in two coupled oscillator populations, deriving new analytical results and analyzing different oscillator types to understand their shape and probability density.

Contribution

It provides a rigorous analysis of chimera state dynamics, including the shape and density evolution, for various oscillator systems, extending previous results and introducing new models.

Findings

Chimera states can be characterized by a closed curve and probability density on it.

The dynamics of the curve shape and density are derived for four oscillator types.

The analysis confirms stability conditions for chimera states in these systems.

Abstract

We consider networks formed from two populations of identical oscillators, with uniform strength all-to-all coupling within populations, and also between populations, with a different strength. Such systems are known to support chimera states in which oscillators within one population are perfectly synchronised while in the other the oscillators are incoherent, and have a different mean frequency from those in the synchronous population. Assuming that the oscillators in the incoherent population always lie on a closed smooth curve $\mathcal{C}$, we derive and analyse the dynamics of the shape of $\mathcal{C}$ and the probability density on $\mathcal{C}$, for four different types of oscillators. We put some previously derived results on a rigorous footing, and analyse two new systems.