Synchronization of coupled systems via parameter perturbations

We consider coupled identical chaotic systems. In some circumstances, the coupled systems synchronize. When this does not happen naturally, we derive methods based on small parameter perturbations which result in synchronous behavior. The perturbations are applied in the neighborhood of a fixed or periodic point in the synchronous subspace which is stable in the normal direction. By keeping iterates in the neighborhood of such points using parameter perturbations, they are naturally drawn closer to the subspace by the stable manifold of the fixed or periodic points. Different ways of varying the parameters are also considered. Methods for two-dimensional systems are first explored and then extended to higher-dimensional systems. Examples are presented to illustrate the methods.