Abstract: Interest in synchronization of chaos has increased because of its possible relevance to secure communication. Recently, papers discussing a more general idea of synchronization have appeared in the literature. We investigate chaossynchronization of nonidentical coupled maps. It is shown that two coupled Logistic maps at different parameter values may not only satisfy stable linear relation but also nonlinear relation with proper coupled fashion. Thestrict analytical proof about it is proposed. This is a new method that don't rely on numerical method completely. We also give the range of the coefficient ofcoupling in generalized synchronization and the functions of the stable linear relation and the stable nonlinear relation.

Key words: chaos, generalized synchronization, couple