Routes to chaos in Duffing oscillator with one potential well

The behavior of the routes to chaos in the AC-driven Duffing oscillator under the variation of excitation amplitude F_AC and frequency ω with damping constant K<0.6 is investigated by numerical experiment. A series of transitions is observed, including a hysteretic jump, symmetry breaking, period-doubling cascade, and escape. The transition boundaries are given in a state diagram in the F_AC vs. ω parameter space. Thus, the transition sequence can be inferred from this diagram. Based on these results, the harmonic balance method and Floquet theory are applied to study the instability of the transition series. It is suggested that all these transitions to chaos can be explained as parametric excitations. In addition, the boundaries in the state diagram can be satisfactorily computed from the conditions with Floquet multiplier μ=±1