Bifurcation of synchronization as a nonequilibrium phase transition

We investigate the transient characteristics of a system that consists of coupled van der Pol oscillators. Special attention is paid to the synchronization dynamics. Numerical simulation reveals that genuine, transient and generalized synchronizations are possible with appropriate interactions. By treating the behaviors of synchronization and asynchronization as distinct phases of dynamic system, we investigate nonequilibrium phase transitions near critical coupling points. The phenomenon of critical slowing-down is studied, and the relevant critical exponent is derived numerically.