On the synchronization of spatially coupled oscillators

Over the past decade, considerable attention has been devoted to the problem of emergence of synchronization patterns in a network of coupled oscillators, which can be observed in a variety of disciplines, from the biological to the engineering fields. In this context, the Kuramoto model is a classical model for describing synchronization phenomena that arise in large-scale systems that exploit local information and interactions. In this work, an extension of such a model is presented, that considers the spatial distances among the oscillator nodes. In detail, coupling strength and spatial conditions are derived, needed to reach phase cohesiveness and frequency synchronization, both in the scenario when a single population of agents is present and when two different populations interact. These theoretical findings are confirmed by extensive numerical Monte Carlo simulations and statistical analysis.