Chimera states and eigen microstates of nonidentical power-law coupled oscillators with heterogeneous phase lag

Chimera state is a special spatiotemporal patterns where coherent and incoherent states coexist, not only related to neuronal evolution but also to diseases such as parkinson, epilepsy, and schizophrenia. In many studies of biological networks, the interaction patterns between individuals often exhibit a scale-free heavy-tailed distribution. Hence, researches into chimera state within scale-free structures may help to understand the close relationship between function and structure in biological systems. Especially in neural systems, interactions between neurons depend on both electrical and chemical signals, naturally involving heterogeneous delay effects. In this study, we introduce power-law coupling, nonidentical natural frequency, and heterogeneous phase delay into the phase oscillator model, exploring the relationship between oscillator coupled strength, power-law exponent, and the emergence of chimera state. Other important thing is that we extend the Eigen Microstate (EM) method to investigate the criticality, attempting to reveal the mechanism of chimera state emergence through the mesoscopic structure of eigen microstate. We find that the critical analysis results of the EM method, relying solely on phase data, are entirely consistent with those obtained by the mean-field method, revealing the inevitable relationship between the emergence of chimera state and the structure-power law coupling. In addition, the spatiotemporal patterns of eigen microstate provide insights into the mesoscopic structure, can be used to distinguish spatial distribution of synchronization, chimera state, and disorder state, as well as their characteristic dynamics of oscillators. This expansion research of the EM method will advance the exploration of criticality in real oscillatory systems.