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

¹ Research Group for Nonlinear Dynamics, Department of Physics, University of Science Unjong-District, Pyongyang, Democratic People's Republic of Korea

^(a) cholung-choe@star-co.net.kp (corresponding author)

Received: 17 June 2021
Accepted: 9 December 2021

Abstract

We consider two populations of coupled oscillators, interacting with 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 Ott-Antonsen 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.