Phase synchronization between two adjacent nodes in amplitude coupled dynamical networks

The present paper aims to investigate the phase synchronization in chaotic oscillator networks by using quantitative indexes. We define two new quantitative indexes, namely the mean phase locking value and mean frequency difference of two adjacent nodes of the network. Lorenz chaotic oscillators with several rotational centers are chosen as networks nodes. We convert the original Lorenz system into the dynamics of amplitude and phase. The chaotic oscillator networks are formed via amplitude coupling. We find that for star-coupled network and small-world network the adjacent oscillation phases are locked. Moreover, phase synchronization definitely comes along with the transition of the mean phase locking value and mean frequency difference by increasing the coupling strength.