Chimera death induced by the mean-field diffusive coupling

TL;DR

This paper demonstrates that chimera death, a state of coexisting coherent and incoherent oscillation death, can be induced in networks with mean-field diffusive coupling, expanding understanding of its formation beyond non-local coupling.

Contribution

It shows that non-local coupling is not necessary for chimera death and introduces a new transition route from synchronized oscillation to chimera death.

Findings

Chimera death can be induced with mean-field diffusive coupling.

A new transition route to chimera death is identified.

Multi-cluster chimera death states are achievable with specific initial conditions.

Abstract

Recently a novel dynamical state, called the {\it chimera death}, is discovered in a network of non locally coupled identical oscillators [A. Zakharova, M. Kapeller, and E. Sch\"oll, Phy.Rev.Lett. 112, 154101 (2014)], which is defined as the coexistence of spatially coherent and incoherent oscillation death state. This state arises due to the interplay of non locality and symmetry breaking and thus bridges the gap between two important dynamical states, namely the chimera and oscillation death. In this paper we show that the chimera death can be induced in a network of generic identical oscillators with mean-field diffusive coupling and thus we establish that a non local coupling is not essential to obtain chimera death. We identify a new transition route to the chimera death state, namely the transition from in-phase synchronized oscillation to chimera death via global amplitude death state. We ascribe the occurrence of chimera death to the bifurcation structure of the network in the limiting condition and show that multi-cluster chimera death states can be achieved by a proper choice of initial conditions.