Bifurcations and global stability of synchronized stationary states in the Kuramoto model for oscillator populations

Abstract

Bistability between synchronized stationary states is shown to occur in large populations of nonlinearly coupled random oscillators (Kuramoto model), governed by trimodal natural frequency distributions. Numerical simulations and a numerical investigation of bifurcating states provide evidence of global stability of such states, subject to unimodal, bimodal, and trimodal frequency distributions. All this may be important in the framework of large superconducting Josephson junctions arrays, as well as of neural networks. © 2001 The American Physical Society.