The maximal Lyapunov exponent for a three-dimensional system driven by white noise

In this paper, based on a perturbation method, the asymptotic expansions of the invariant measure and the maximal Lyapunov exponent for a three-dimensional system excited by a white noise are evaluated. All possible singular boundaries of the first or the second kind that exist in the one-dimensional phase diffusion process are considered and the results of the maximal Lyapunov exponent are obtained. In addition, the P-bifurcation behaviors are investigated.