Heterogeneous phase oscillators encoded by simplexes under coupling strength symmetry breaking: Optimal synchronization and abrupt desynchronization

Abstract

Recent advances demonstrate that the collective dynamics of heterogeneous phase oscillators ensemble encoded by simplexes play an important role in the storage of information in the human brain. In this letter, we discuss the collective dynamics of heterogeneous phase oscillator networks encoded by simplexes under coupling strength symmetry breaking. Specifically, the strength of the asymmetric coupling between the oscillators is redefined by the degree of the oscillators under 1- and 2-simplex encoding and the heterogeneity parameter. Here, we discuss the effect of different degrees of coupling strength symmetry breaking on the synchronization capability of the system. In particular, we find that proper coupling strength symmetry breaking is beneficial to enhance the synchronization capability of the system. We capture an interesting phenomenon in heterogeneous phase oscillator networks that distinguish symmetric coupling under 1- and 2-simplex encoding, i.e., the system exhibits significant desynchronization behavior under strong symmetry breaking of the coupling strength. Finally, for a fixed heterogeneity parameter and coupling strength assignment probability, we give the optimal intrinsic frequency assignment scheme based on the spectral decomposition of the composite Laplace matrix of the underlying network. Theoretically, these findings may help us to better understand the collective dynamics in heterogeneous phase oscillator networks encoded by simplexes under asymmetric coupling that are prevalent in the real world. In particular, they provide inspiration and guidance for optimizing the synchronization of heterogeneous phase oscillator networks encoded by simplexes under coupling strength symmetry breaking.