Phase transition to chimera state in two populations of oscillators interacting via a common external environment

Abstract

Abstract We consider two populations of coupled oscillators, interacting each other through a common external environment. The external environment is synthesized by the contributions from all oscillators of both populations. Such indirect coupling via an external medium arises naturally in many fields, e.g., dynamical quorum sensing in coupled biological and chemical systems. We analyze the existence and stability of a variety of stationary states on the basis of the OttAntonsen reduction method, which reveals that the interaction via an external environment gives rise to unusual collective behaviors such as the uniform drifting, non-uniform drifting and chimera states. We present a complete bifurcation diagram, which provides the underlying mechanism of the phase transition towards chimera state with the route of incoherence → uniform drift → non-uniform drift → chimera.