Transient and steady-state responses in a self-sustained oscillator with harmonic and bounded noise excitations

The transient and steady-state responses of a self-sustained oscillator under harmonic and bounded noise excitations are studied. By means of the generalized cell mapping method under stochastic excitation, the evolution processes of transient and steady-state probability density functions are obtained. By comparison to Monte Carlo results, the method is verified as valid and accurate for analyzing the response of nonlinear stochastic dynamical systems. Furthermore, it is found that as the amplitude of bounded noise and the Wiener process intensity vary, the number of peaks of the steady-state probability density function changes, indicating that stochastic P-bifurcation occurs.