On strong and weak chaotic partial synchronization

We study coupled nonlinear dynamical systems with chaotic behavior in the c ase when two or more (but not all) state variables synchronize, i.e. conver ge to each other asymptotically in time. It is shown that for symmetrical s ystems, such partial chaotic synchronization is usually only weak, whereas with nonsymmetrical coupling it can be strong in large parameter ranges. Th ese facts are illustrated with systems of three coupled one-dimensional map s, for which a rich variety of different "partial chaotic synchronizing" ph enomena takes place.