SYNCHRONOUS VERSUS ASYNCHRONOUS DYNAMICS IN SPATIALLY DISTRIBUTED SYSTEMS

Many prototypical models of spatially extended systems that are capable of complex spatiotemporal dynamics impose a finite discretization window of space and time. For such models, it is important to determine to what extent the specific procedure which is used to update local states affects the overall regimes, as the latter might turn out to be artifacts due to an unrealistic digitalization of the world. The chances of generating spatiotemporal patterns with no counterparts in the physical world are particularly high with granular space-time models that rely on a synchronous evolution of distributed states, as such synchronous evolution is found in nature most typically in systems governed by evolution laws in the form of partial differential equations. We show this possibility to be the case for the regimes produced in coupled map lattices, as markedly different dynamics arise when the standard synchronous model is made asynchronous. By quantifying the degree of mutual asynchrony in the system, signatures of asynchronous spatiotemporal dynamics are unraveled and further characterized in terms of simple stability measures.