Synchronization of nonlinear systems with distinct parameters: Phase synchronization and metamorphosis

Rather than the synchronization between identical chaotic systems, the "phase synchronization" among two or many nonlinear systems with distinct nonlinear parameters is investigated. It is observed that the dynamics of globally coupled $N_1$ periodic and $N_2$ chaotic systems can be reduced to that between matrix-coupled chaotic and periodic systems as the result of a two-step realization of the synchronization among the former systems. The same situation holds even for the array of distinct systems with a nearest-neighbor interaction.