Potential dependence of the bifurcation structure in generalized Duffing oscillators

The features of various bifurcations in forced Duffing oscillators are extensively investigated by means of numerical simulation. Some common features in four types of potential well are found. With reference to the transition boundaries in parameter space, the influences of local symmetry properties of the potential well on the bifurcation routes are indicated and definite functional forms of the border line in {ω}-k space separating the region with simple stable period-1 solutions from the region with complicated solutions are determined. A method combining Floquet theory with harmonic balance is presented to describe the mechanism of the transitions.