GENERALIZED SYNCHRONIZATION, PREDICTABILITY, AND EQUIVALENCE OF UNIDIRECTIONALLY COUPLED DYNAMICAL-SYSTEMS

Necessary and sufficient conditions for the occurrence of generalized synchronization of unidirectionally coupled dynamical systems are give n in terms of asymptotic stability. The relation between generalized s ynchronization, predictability, and equivalence of dynamical systems i s discussed. All theoretical results are illustrated by analytical and numerical examples. In particular, the existence of generalized synch ronization in the case of parameter mismatch between coupled systems l eads to a new interpretation of recent experimental results. Furthermo re, the possible application of generalized synchronization for attrac tor reconstruction in nonlinear time series analysis is discussed.