Average dynamics of a finite set of coupled phase oscillators

Abstract

Many fields of physics deal with the macroscopic description of large systems, composed by N interacting members. In some cases, it is possible to address them in terms of a mean field theory, designed to describe the parameters accounting for the average behavior of the system. This approach requires the study of a surrogate problem, consisting of an infinite number of interacting elements. In this work, we study the macroscopic dynamic of a system of N non-linear interacting units. For that, we use topological tools in order to compare the system of N units with its surrogate with infinite elements. We report, for a particular problem, a minimum number of units required for the two systems to be topologically equivalent.