Synchronization domains in arrays of chaotic homoclinic systems

With reference to experiments on a CO₂ laser with feedback, we summarize the main features of chaotic orbits homoclinic to a saddle focus, and then face the problem of an array of coupled identical systems of this kind. We first investigate the dynamics of a closed chain of unidirectionally coupled oscillators in a regime of homoclinic chaos. The emerging synchronization regimes show analogies with the experimental behavior of a single chaotic laser self synchronized by a delayed feedback. Then we explore the response of an open chain of bidirectionally coupled chaotic homoclinic systems to external periodic stimuli. When one end of the chain is driven by a periodic signal, the system propagates a phase synchronization state in a certain range of coupling strengths and external frequencies. When two simultaneous forcings are applied at different points of the array, a rich phenomenology of stable competitive states is observed, including temporal alternation and spatial coexistence synchronization domains.