Moment Lyapunov exponent of three-dimensional system under bounded noise excitation

In the present paper, the moment Lyapunov exponent of a codimensional two-bifurcation system is evaluted, which is on a three-dimensional central manifold and subjected to a parametric excitation by the bounded noise. Based on the theory of random dynamics, the eigenvalue problem governing the moment Lyapunov exponent is established. With a singular perturbation method, the explicit asymptotic expressions and numerical results of the second-order weak noise expansions of the moment Lyapunov are obtained in two cases. Then, the effects of the bounded noise and the parameters of the system on the moment Lyapunov exponent and the stability index are investigated. It is found that the stochastic stability of the system can be strengthened by the bounded noise.