On the synchronization of heterogeneous phase oscillator networks

Abstract

This paper presents a study on synchronization behaviors in phase oscillator networks where the oscillators are interconnected through a general nonlinear function and their interconnections are bidirectional. Consequently, we investigate two contexts namely symmetric and asymmetric couplings among oscillators. In both cases, we show that if the coupling strengths are greater than some specific levels then the frequencies of oscillators in the network are synchronized. Furthermore, the synchronization rate is pointed out. Lastly, several numerical examples are presented to illustrate the theoretical results.