Analytical and numerical results for entrainment in large networks of coupled oscillators

In this paper we consider large networks of coupled oscillators. We choose to illustrate this using a general class of range dependent networks where the pairwise coupling is a probabilistic function of distance (range) between the nodes, and each node represents an oscillator with its own intrinsic phase and natural frequency of oscillation. Range dependent networks exhibit the "small world" phenomenon, being effectively superpositions of many networks each operating over different range lengths. We provide an asymptotic analysis in terms of a network coupling parameter that gives a simple analytic description of the coupled dynamics and which agrees well with numerical experiments.