The drift of chimera states in a ring of nonlocally coupled bicomponent phase oscillators

School of Science, Beijing University of Posts and Telecommunications - Beijing 100876, PRC

^(a) jzyang@bupt.edu.cn

Received: 12 December 2018
Accepted: 7 March 2019

Abstract

The chimera state is a fascinating symmetry-breaking dynamical state in a network of coupled oscillators. In this paper, we study a ring of nonlocally coupled bicomponent phase oscillators in which oscillators with natural frequency ω₀ are motionless and oscillators with natural frequency −ω₀ are moving at the velocity v along the ring. In response to the movement of oscillators, chimera states in the two subpopulations drift along the ring. For small ω₀, the two chimera states are synchronized with their coherent oscillators oscillate at the same frequency and drifting at the same velocity proportional to v. For large ω₀, there exist several dynamical regimes depending on v. At sufficiently low v, the coherent oscillators in the two subpopulations move at the same velocity much higher than v. In contrast, at high v, the chimera state in the moving oscillators drifts at v while that in the motionless oscillators it stays roughly stationary. In between, the drifting velocities in the moving and the motionless oscillators get separated from each other.