Coexistence of synchronized and desynchronized patterns in coupled chaotic dynamical systems

Abstract

We analyse the synchronous chaos and its stability in coupled map lattices and coupled nonlinear oscillators. The existence of desynchronized patterns such as standing wave like spatiotemporal periodic patterns within the critical size limit is identified for some sets of random initial conditions. The emergence of such patterns is explained using the concept of controlling of chaos. In the case of coupled map lattices, an expression for standing wave like pattern is given in terms of unstable periodic orbits of the isolated map. Finally, the role of initial conditions on the existence of multiple stable states in both coupled map lattices and coupled oscillators is studied.