Embedded invariant manifolds and ordering of chaotic synchronization of diffusively coupled systems

Results of a qualitative analysis of an array of diffusively coupled identical continuous time dynamical systems are presented. The effect of partial chaotic synchronization are investigated via the linear invariant manifolds of the corresponding differential equations. Existence of various synchronization manifolds, a hierarchy and embedding of the manifolds of the coupled system are discovered. The general rigorous results are illustrated through examples of coupled Rossler systems