TORUS DOUBLING IN FOUR WEAKLY COUPLED OSCILLATORS

Abstract

We present evidence of torus doubling in systems of four weakly coupled oscillators. We assume that the oscillators are dissipative, so the system has an attracting invariant four-torus giving a Poincaré map on a section which is a three-torus. Using averaging, the asymptotic dynamics can be approximated by a flow on a three-torus. Thus it is possible to have period doubling in the averaged flow, corresponding to torus doubling in the unaveraged system; this is not possible for three or fewer oscillators in the weakly coupled limit. We observe torus-doubling bifurcations for a three-torus map and for a system of four coupled electronic oscillators.