Criticality in transient behavior of coupled oscillator system towards Chimera and Synchronization

Abstract Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems. While how the system is steering towards different final destinies upon spatially localized perturbation is still unknown. Through systematic numerical analysis of the evolution of the spatiotemporal pattern of the multi-cluster chimera states, we uncover a critical behavior of the system in transient time towards either chimera or synchronization as the final stable state. Based on adequate verification, we fit and analyze the distribution of the transient time, and observe power-law variation process as perturbation strengths approaches the critical point, which divided the phase of stable chimera and synchronization states. Moreover, the comparison between different clusters systems shows that the critical points of odd and even clusters converge in proportional like sequences as the cluster number approaches infinity, implying that this critical behavior can be modeled and enabling the articulation of a phenomenological model. Our work explores the criticality in transient behavior as well as the phase transition from chimera to synchronization under increasing perturbation, which may shed new insights to controlling coupled oscillator system with the help of perturbation through inducing phase transition between symmetry and asymmetry self-organized states.