Symmetry-breaking perturbations and strange attractors

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with symmetry-breaking disturbances. Even a slight fixed asymmetry in the perturbation may cause a substantial change in the asymptotic behavior of the system, e.g., transitions from two-sided to one-sided strange attractors as the other parameters are varied. Moreover, slight asymmetries may cause substantial differences in the relative size of the basins of attraction of the two wells. These changes seem to be associated with homoclinic bifurcations. Numerical evidence indicates that strange attractors appear near curves corresponding to specific secondary homoclinic bifurcations. These curves are found using analytical perturbational tools.