Noise perturbations of a nonlinear system with multiple steady states
This paper concerns a Duffing oscillator governed by the stochastic differential equation \(x''(t)+ 2\eta \omega_ 0 x'(t)+ \gamma \omega_ 0^ 2 x^ 3 (t)= \Gamma\cos \Omega t+ \zeta(t)\), where \(\zeta(t)\) is a small, white Gaussian noise. Attractors yielding two stable oscillatory states are identified, and the steady state probability density function of the fluctuations about these stable states is approximated. The time spent in a given stable state is examined by approximating the mean first passage time from its domain of attraction to that of the other state. Simulation results are presented that agree well with results obtained by using these approximations.
steady state probability density function
scientific article; zbMATH DE number 707513