Properties of phase locking with weak phase-coherent attractors

In coupled chaotic oscillators, the synchronization with weak phase-coherent attractors is different from that with strong phase-coherent ones. The properties of phase locking for weak phase-coherent attractors are studied with examples. For a small parameter mismatch, transition to phase locking is close to the position where the second zero Lyapunov exponent becomes negative and one of the positive Lyapunov exponents becomes zero simultaneously. However. for a large mismatch, it occurs at a farther position evidently. These results lead to a better understanding of the properties of synchronization in coupled oscillators. (C) 2001 Published by Elsevier Science B.V.