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Four Examples of Phase Synchronization in Oscillator Networks

Considerable attention has been devoted to the different synchronization phenomena [1] in biology. Such as complete synchronization, cluster synchronization, anti-synchronization, and so on[2, 3, 4, 5, 6]. During recent twenty years, phase synchronization has attracted much interest. Many dynamical behaviors in biological systems can be explained by phase synchronization finally[8]. This synchronization is different from the classical concept of synchronization. In the research of phase synchronization, one of the simplest model is Kuramoto model[7]. The Kuramoto model describe the coupling dynamics of a set of n oscillators. The Kuramoto model is given by: