  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.
