On stationary probability density and maximal Lyapunov exponent of a co-dimension two bifurcation system subjected to parametric excitation by real noise

In this paper, the asymptotic expansions of the maximal Lyapunov exponents for a co-dimension two-bifurcation system which is on a three-dimensional center manifold and is excited parametrically by an ergodic real noise are evaluated. The real noise is an integrable function of an n-dimensional Ornstein-Uhlenbeck process. Based on a perturbation method, we examine almost all possible singular boundaries that exist in one-dimensional phase diffusion process. The comparisons between the analytical solutions and the numerical simulations are given. In addition, we also investigate the P-bifurcation behavior for the one-dimensional phase diffusion process. The result in this paper is a further extension of the work by Liew and Liu 1].