Using optimal control theory to identify network structures that foster synchrony

Network structures are known to influence a population’s propensity to synchronize. Previous attempts to identify synchrony promoting structures have focused on homogeneous populations. We use optimal control theory to construct networks that allow heterogeneous populations to maintain high levels of synchrony, explore the relationship between population heterogeneity and the structure of the optimal networks, and identify salient optimal network features that may enhance synchrony. In particular, we identify a new parameter, the average strength of neighbors, that may foster synchrony and observe that repulsion, in addition to attraction, can foster synchrony.

► We construct networks that are optimized to preserve synchrony in a heterogeneous population. ► We identify network structures that foster synchrony. ► We find that the average strength of neighbors is a parameter that characterizes optimal networks. ► We examine the relation between population heterogeneity and optimal network heterogeneity. ► Optimal networks exhibit substantial heterogeneity even when a population is almost homogeneous.