Generalized synchronization, frequency-locking and phase-locking of coupled sine circle maps

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sin e circle maps. We specify a range of parameters for which the coupled syste m achieves generalized synchronization. We also investigate the relation be tween generalized synchronization, predictability and equivalence of dynami cal systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is pred ictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coup ling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those o f the individual map and are independent of the coupling strength.