Anomalous synchronization of spatialy extended chaotic systems in the presence of asymmetric coupling

This paper describes the effects of an asymmetric coupling in the synchronization of two spatially extended systems. Namely, we report the consequences induced by the presence of asymmetries in the coupling configuration of a pair of one-dimensional fields obeying Complex Ginzburg–Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of enhancing synchronization and play a crucial role in setting the threshold for the appearance of the synchronized dynamics, as well as in selecting the statistical and dynamical properties of the synchronized motion. We discuss the process of synchronization in the presence of asymmetries by using some analytic expansions valid for a regime of soft spatial temporal chaos (i.e. phase turbulence regime). The influence of phase singularities that break the validity of the analysis is also discussed.