Synchronization–desynchronization transitions in networks of circle maps with sinusoidal coupling

Abstract

Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention had been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.

Stability and multistability of synchronization in networks of coupled phase oscillators

“…This is another interesting topic that is discussed elsewhere. [36] We theoretically discuss the stability of the synchronous state and verify that the in-phase state keeps locally stable for strong couplings. Moreover, multistability in phase space implies the existence of other metastable states that may coexist with the IPS in the synchronous regime.…”