Sign-independent synchronization in unidirectionally coupled chaotic systems

In this paper, a synchronization scheme independent of the sign of the driving signal is developed and analyzed. The corresponding synchronization phenomenon is termed sign-independent synchronization in this context. In our coupling scheme, an even coupling function is used at the response in an attempt to make the response independent of the sign of the driving signal. Furthermore, the Jacobian (and hence the stability) defined on the synchronization manifold of sign-independent synchronization systems can be made identical to that of a corresponding active-passive decomposition system. Hence the conditions for achieving stable sign-independent synchronization can be generally established as a trivial case in unidirectionally coupled chaotic systems where the method of active-passive decomposition is applicable. Through numerical experiments performed on both continuous and discrete systems, we demonstrate that in-phase synchronization can be maintained even if the phase of the driving signal is randomly inverted. We believe the proposed chaotic synchronization will find important application in digital communications.