Self-emerging symmetry breakings in a two-population network of phase oscillators interacting via an external environment

Abstract

A network consisting of two populations of phase oscillators with heterogeneous intra- and inter-population couplings is known to be the simplest model for a chimera state. In this work, we generalize this chimera model by adding the indirect interaction through an external environment in the coupling scheme. The dynamical external environment is driven by the contributions from all oscillators in both populations and then it acts as a controller on the two-population chimera system. We show that a variety of symmetry-broken states including the chimera could emerge as a unique attractor due to the indirect interaction via an environment. Moreover, different states, ranging from the incoherence to the uniform drift, non-uniform drift, chimera and coherent states, can effectively be switched by adjusting the indirect coupling strength. We report on exotic behaviors such as the so-called inclined coherence, which corresponds to an intermediate state between the coherent and π-coherent states, as well as the cluster-coherent and alternating drift states as new types of symmetry breakings. To explain the mechanisms under these phase transitions between different collective behaviors, we reduce our model in the continuum limit to a low-dimensional system by applying the Ott–Antonsen approach and present stability diagrams on the basis of analyzing the reduced system. It is demonstrated numerically that the self-emerging chimera states persist for the small-size systems as well.