An analytical study in coupled map lattices of synchronized states and traveling waves, and of their period-doubling cascades

Several theorems are demonstrated that determine sufficient conditions for the existence of synchronized states (both periodical and chaotic) and also of traveling waves in a CML. The existence of period-doubling cascades for the described patterns are also established. Thus, many numerical procedures in CML are given rigorous mathematical foundations. Furthermore, numerical results in CML published to date, are much more general than previously thought.