Complete synchronization of chaotic maps under advection

Abstract

We explore the emergence of complete synchronization under advection in a linear array of chaotic maps. The couplings decay algebraically with the distance between maps, covering from nearest-neighbor to infinite-range interactions, while the update protocol allows us to scan continuously from nondelayed to one-time-delayed dynamics. When the couplings are symmetric (diffusive) and the update is nondelayed, it is well known that chaotic orbits can synchronize if the range of interactions is long enough, while the inclusion of delays allows complete synchronization of a variety of other trajectories besides chaotic ones. Now we investigate through numerical simulations and theoretical analysis how the inclusion of antisymmetric couplings (advection) affects this scenario, showing the interplay among advection, the range of the interactions, and delay. In general, advection reduces the region in parameter space where completely synchronized states are stable, without affecting the nature of the orbits. The presence of delay can lessen the destabilizing effect of advection, such that synchronization is still possible even when couplings are short-range, for a suitable contribution of the delay, but globally coupled lattices are also affected when delayed responses predominate.