Figure 1
(Upper) Bifurcation diagram of the noise-free (σ = 0) Duffing oscillator showing a bistability of limit cycles. The different colors, blue and yellow, represent each limit cycle, S2 and S1, respectively. The state variable \(\dot{x}\) (nT) is the T-shift map of the limit cycle variable, \(\dot{x}\). The points F1 and F2 mark the parameters where catastrophic shift occurs, A1c = 17.2295 and A2c = 8.2250 are the corresponding critical parameter values. The other system parameters are settled in d = 0.3, ω = 0.5. (Bottom) The asymptotic generalized winding numbers, w∞, of each limit cycle in the parameter interval. The colors correspond to the respective limit cycles.
