Critical slowing down in synchronizing nonlinear oscillators

We investigate the transient properties of two van der Pol oscillators that are interacting with various types of couplings. As the coupling constant varies, the transient dynamics changes qualitatively and new intermediate or asymptotic attractors may appear. This can be considered as a kind of dynamic phase transition in nonequilibrium systems. It is interesting to find that two nonlinear oscillators could be phase locked and synchronized with appropriate couplings, and that critical slowing down might occur near the boundaries of the synchronization domain. Besides the genuine asymptotic synchronization, we also observe the transient synchronization that occurs only momentarily. For both classes of synchronization, the relevant exponent describing the slowing down dynamics is found to be equal to a mean field value of unity. [S1063-651X(98)11111-X].