Bifurcation structure of two coupled periodically driven double-well Duffing oscillators

The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force f and its frequency Ω. We first examine the stability of the steady-state in linear response, and classify the different types of bifurcation likely to occur in this model. We then explore the complex behavior associated with these bifurcations numerically. Our results show many striking departures from the behavior of coupled driven Duffing oscillators with single-well potentials, as characterized by Kozłowski et al. [Phys. Rev. E 51 (1995) 1861]. In addition to the well-known routes to chaos already encountered in a one-dimensional Duffing oscillator, our model exhibits imbricated period-doubling of both types, symmetry-breaking, sudden chaos and a great abundance of Hopf bifurcations, many of which occur more than once for a given driving frequency. We explore the chaotic behavior of our model using two indicators, namely Lyapunov exponents and the power spectrum. Poincaré cross-sections and phase portraits are also plotted to show the manifestation of coexisting periodic and chaotic attractors including the destruction of T2 tori doubling.