Asynchronous updating of coupled maps leads to synchronization

Abstract

We investigate the spatiotemporal dynamics of two dimensional coupled map lattices, in the strong coupling phase, evolving under updating rules incorporating varying degrees of asynchronicity. Interestingly, we observe that parallel updates never allow synchronization among the sites, while asynchroncity has the effect of opening up windows in parameter space where the synchronized dynamics gains stability. As asynchronicity increases, the parameter range supporting synchronization gets rapidly wider. Detailed numerics, including bifurcation diagrams and patterns formed en route to synchronization, are reported. We also attempt a mean-field analysis of the system in order to try and account for the stability of the spatiotemporal fixed point under asynchronous updates.