Numerical stability of chaotic synchronization using a nonlinear coupling function

Nonlinear coupling has been used to synchronize some chaotic systems. The difference evolutional equation between coupled systems, determined via the linear approximation, can be used to analyze the stability of the synchronization between drive and response systems. According to the stability criteria the coupled chaotic systems are asymptotically synchronized, if all eigenvalues of the matrix found in this linear approximation have negative real parts. There is no synchronization, if at least one of these eigenvalues has positive real part. Nevertheless, in this paper we have considered some cases on which there is at least one zero eigenvalue for the matrix in the linear approximation. Such cases demonstrate synchronization-like behavior between coupled chaotic systems if all other eigenvalues have negative real parts.