Invariant manifolds and cluster synchronization in a family of locally coupled map lattices

This paper presents an analysis of the invariant manifolds for a general fa mily of locally coupled map lattices. These manifolds define the different types of full, partial, and antiphase chaotic synchronization that can aris e in discrete dynamical systems. Existence of various invariant manifolds, self-similarity as well as orderings and embeddings of the manifolds of a c oupled map array are established, A general variational equation for the st ability analysis of invariant manifolds is derived, and stability condition s for full and partial chaotic synchronization of concrete coupled maps are obtained, The general results are illustrated through examples of three co upled two-dimensional standard maps with damping.