Bifurcation and Chaos in Coupled Periodically Forced Non-identical Duffing Oscillators

Abstract

We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we show that our model presents phenomena which were not observed in coupled periodically forced Duffing oscillators with identical potentials. In the regime of relatively weak coupling, bubbles of bifurcations and chains of symmetry-breaking are identified. For much stronger couplings, Hopf bifurcations born from orbits of higher periodicity and supercritical Neimark bifurcations emerge. Moreover, tori-breakdown route to a strange non-chaotic attractor is also another highlight of features found in this model.