Frequency Locking in Countable Cellular Systems, Localization of (Asymptotic) Quasi-Periodic Solutions of Autonomous Differential Systems.

International audienceWe address the question of frequency locking in coupled differential systems and of the existence of some quasi-periodic solutions of a certain kind of differential systems. Those systems are named "cellular systems" quite generally as they deal with countable numbers of coupled systems in some general Banach spaces. Moreover, the inner dynamics of each subsystem does not have to be specified. We reach some general results about how the frequency locking phenomenon is related to the structure of the coupling map. Those results can be restated in terms of localization of a certain type of quasi-periodic solution of differential systems that may be seen as cellular systems. This paper gives some explanations about how and why synchronized behaviors naturally occur in a wide variety of complex systems