Synchronization in small assemblies of chaotic systems

In this paper we investigate the behavior of small networks of van der Pol-Duffing chaotic oscillators that are connected through local, although not weak, coupling through a recently introduced [Phys. Rev. E 52, R2145 (1995)] extension of the Pecora-Carroll synchronization method. The method allows one to design a variety of settings with different ways of connecting a number of low-dimensional circuits. It is shown that a variety of different behaviors can be obtained, depending, among other factors, on the symmetry of the connections and on whether the oscillators are identical or different. One may cite the emergence of coherent behavior (a single cluster), either chaotic or periodic, as stemming just from interaction among the different chaotic units, although several coexisting clusters are found for other settings.