Chimeras in networks with purely local coupling

TL;DR

This paper demonstrates the existence of chimera states in networks with purely local diffusive coupling, supported by numerical simulations and analytical boundary analysis in the continuum limit.

Contribution

It introduces three local-coupling networks that support chimera states and provides an analytical approach to determine their existence boundaries.

Findings

Chimera states can occur in networks with only local coupling.

Analytical boundaries for chimera existence are derived in the continuum limit.

Numerical simulations confirm the presence of chimera states in the proposed networks.

Abstract

Chimera states in spatially extended networks of oscillators have some oscillators synchronised while the remainder are asynchronous. These states have primarily been studied in networks with nonlocal coupling, and more recently in networks with global coupling. Here we present three networks with only local coupling (diffusive, to nearest neighbours) which are numerically found to support chimera states. One of the networks is analysed using a self-consistency argument in the continuum limit, and this is used to find the boundaries of existence of a chimera state in parameter space.