Sign-independent synchronization in unidirectionally coupled chaotic systems

In this paper, a synchronization scheme independent of the sign of the driv ing signal is developed and analyzed. The corresponding synchronization phe nomenon is termed sign-independent synchronization in this context. In our coupling scheme, an even coupling function is used at the response in an at tempt to make the response independent of the sign of the driving signal. F urthermore, the Jacobian (and hence the stability) defined on the synchroni zation manifold of sign-independent synchronization systems can be made ide ntical to that of a corresponding active-passive decomposition system. Henc e the conditions for achieving stable sign-independent synchronization can be generally established as a trivial case in unidirectionally coupled chao tic systems where the method of active-passive decomposition is applicable. Through numerical experiments performed on both continuous and discrete sy stems, we demonstrate that in-phase synchronization can be maintained even if the phase of the driving signal is randomly inverted. We believe the pro posed chaotic synchronization will find important application in digital co mmunications. [S1063-651X(99)09111-4].