Stability criterion for projective synchronization in three-dimensional chaotic systems

Projective synchronization, in which the state vectors synchronize up to a scaling factor, has recently been observed in coupled partially linear chao tic systems (Lorenz system) under certain conditions. In this Letter, we pr esent a stability criterion that guarantees the occurrence of the projectiv e synchronization in three-dimensional systems. By applying the criterion t o two typical partially linear systems (Lorenz and disk dynamo), it shows t hat only some parameters play the key role in influencing the stability. Pr ojective synchronization only happens when sigma > -1 for the Lorenz and mu > 0 for the disk dynamo. (C) 2001 Elsevier Science B.V. All rights reserve d.