Identical Oscillator Networks with Symmetry

Abstract

This is a review of some theoretical and experimental results concerning networks of identical oscillators with Sn symmetry under a hypothesis of weak coupling. Such networks have a global or mean field coupling so that the network is symmetric under any interchange permuting the oscillators. The phase space is highly structured by the weak coupling and symmetry, and allows some quite unusual dynamical transitions to take place. Upon forcing the system, there is experimental evidence of symmetric bifurcations of chaotic at tractors.