An Approach to Analyse Phase Synchronization in Oscillator Networks with Weak Coupling

We study phase synchronization in oscillator networks through phase reduced method. The dynamics of networks is reduced to phase equations
by this method. Analysing the phase equations through the master stability function method, one obtains that the oscillators with identical frequency can be in-phase synchronized by weak balanced coupling. Similarly, the problem of frequency synchronization of oscillators with different frequencies is transformed to the existence of a locally asymptotically stable equilibrium of the phase error system.