First-passage problem for Coupled Duffing-van der Pol Systems Subject to Gaussian Excitation

In this paper, the stochastic average method for stochastic and dissipative quasi-non-integrable Hamiltonian system is applied to study the first-passage problem of coupled Duffing-van der Pol system subject to Gaussian white noise excitation. First, a backward Kolmogorov equation for the conditional reliability function and a generalized Pontryagin equation for the conditional moment of the first-passage time are established. Then according to the classification of the boundary conditions and initial conditions of these two kinds of equations, the reliability of system response under external excitation combined with parametric excitation and pure parametric excitation are analyzed respectively in detail. At last, numerical results for reliability function, the probability of first-passage time and mean first-passage time of system in virtue of figures.