Bistability of globally synchronous and chimera states in a ring of phase oscillators coupled by a cosine kernel

Abstract

Chimera states, where coherent and incoherent activity coexists in homogeneous networks, have been a focus of synchronization theory studies over many years. In this paper, we consider dynamical regimes in a ring of phase oscillators coupled by a cosine kernel using new synchronization criteria - adaptive coherence measure (ACM). We show that the ACM-criterion can be successfully applied for phase oscillator networks. Our measure allowed us to partition the parameter plane into regions along collective dynamics. We discovered that, for the certain parameter sets, there is the bistability between globally synchronous and chimera states. This bistability allows to control network dynamics by changing the initial conditions and/or the external forcing. This shows the potential flexibility in control over complex network behaviors.