[en] We study the bifurcation structure and the synchronization of a double-well Duffing oscillator coupled to a single-well one and subjected to periodic forces. Using the amplitudes and the frequencies of these driving forces as control parameters, we show that our model presents phenomena which were not observed in a similar system but 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, as well as subcritical and supercritical Neimark bifurcations emerge. Varying the coupling strength, we also find a threshold for which the system remains quasiperiodic. Moreover, tori-breakdown route to a strange non-chaotic attractor is another highlight of features found in this model. In two parameter diagrams, regions of chaos and quasiperiodicity are clearly identified. Finally, threshold parameters for which synchronization occurs have been found