Stretching Folding Twisting in the Driven Damped Duffing Device

Abstract

The results presented here represent another step in our attempt to provide a topological understanding of the behavior of nonlinear dynamical systems. The conditions under which “bifurcation bubbles” exist for a dynamical system has always been a mystery. They occur, for example, in the driven Duffing oscillator. We began by computing the Relative Rotation Rates for the periodic orbits of the Duffing oscillator in order to determine the systematics of “bifurcation bubbles.” The systematics which we have discovered have led to an increased understanding of the mechanics responsible for the bifurcation phenomena seen in driven nonlinear oscillators. In particular, these phenomena can be classified as local bifurcation phenomena and global bifurcation phenomena in a natural way.