Partial synchronization and clustering in a system of diffusively coupled chaotic oscillators

We examine the problem of partial synchronization (or clustering) in diffus ively coupled arrays of identical chaotic oscillators with periodic boundar y conditions. The term partial synchronization denotes a dynamic state in w hich groups of oscillators synchronize with one another, but there is no sy nchronization among the groups. By combining numerical and analytical metho ds we prove the existence of partially synchronized states for systems of t hree and four oscillators. We determine the stable clustering structures an d describe the dynamics within the clusters. Illustrative examples are pres ented for coupled Rossler systems. At the end of the paper, synchronization in larger arrays of chaotic oscillators is discussed. (C) 2001 IMACS. Publ ished by Elsevier Science B.V. All rights reserved.