Self-synchronization of populations of nonlinear oscillators in the thermodynamic limit

• DOI: 10.1007/bf01019689
• Publication Date: 2005-01-19T12:36:04Z
• Authors: Luis L. Bonilla; Jos� M. Casado; Manuel Morillo
• Keywords: Thermodynamic limit; Stationary state

A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase transition from a stationary to a time-periodic probability density. Below the transition line, the population of oscillators is in a quiescent state with order parameter equal to zero. Above the transition line, there is a state of collective rhythmicity characterized by a time-periodic behavior of the order parameter and all moments of the probability distribution. The information entropy of the ensemble is a constant both below and above the critical line. Analytical and numerical analyses of the model are provided.