Chimera States in a Two-Population Network of Coupled Pendulum-Like Elements

TL;DR

This paper investigates the existence of chimera states in a two-population network of pendulum-like phase oscillators with inertia, demonstrating their presence for small mass values and providing a reduced model explanation.

Contribution

It introduces a novel model of coupled pendulum-like elements with inertia and shows chimera states occur at small mass values, supported by numerical and analytical reduction methods.

Findings

Chimera states exist in the system for small mass values.

A reduced damped pendulum model explains the chimera states.

Numerical evidence supports the theoretical analysis.

Abstract

More than a decade ago, a surprising coexistence of synchronous and asynchronous behavior called the chimera state was discovered in networks of nonlocally coupled identical phase oscillators. In later years, chimeras were found to occur in a variety of theoretical and experimental studies of chemical and optical systems, as well as models of neuron dynamics. In this work, we study two coupled populations of pendulum-like elements represented by phase oscillators with a second derivative term multiplied by a mass parameter $m$ and treat the first order derivative terms as dissipation with parameter $\epsilon>0$. We first present numerical evidence showing that chimeras do exist in this system for small mass values $0<m<<1$. We then proceed to explain these states by reducing the coherent population to a single damped pendulum equation driven parametrically by oscillating averaged quantities related to the incoherent population.