Noise-induced chaos in Duffing oscillator with double wells

Stochastic Melnikov method is employed to predict noise-induced chaotic response in the Duffing oscillator with double wells. The safe basin is simulated to show the noise-induced fractal boundary. Three cases are considered: harmonic excitation, both harmonic and Gaussian white noise excitations, and Gaussian white noise excitation. The leading Lyapunov exponent estimated by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can be fractal even if the system is excited only by external Gaussian white noise.