有界噪声参激一类三维系统的矩Liapunov指数

对于一类三维中心流形上受有界噪声参激的余维2分岔系统，计算了它的矩Liapunov指数．根据随机动力系统理论，首先建立了系统矩Liapunov指数求解的特征值问题，然后由奇异摄动法，得到了弱噪声展开的矩Liapunov指数的二阶渐近解析表达式和数值结果．接着进一步研究了有界噪声和系统参数对矩Liapunov指数和稳定指标的影响．结果表明:系统的随机稳定性有被有界噪声加强的可能性．

Moment Liapunov Exponent of a Three-Dimensional System Under Bounded Noise Excitation

The moment Liapunov exponent of a co-dimension two bifurcation system was evaluated, which was on a three-dimensional central manifold and was subjected to a parametric excitation by a bounded noise.Based on the theory of the stochastic dynamics,the eigenvalue problem governing the moment Liapunov exponent was established.Through a singular perturbation method,the explicit asymptotic expressions or numerical results of the second-order,weak noise expansions of the moment Liapunov are obtained for two cases.Then the effects of the bounded noise and the parameters of the system on the moment Liapunov exponent and the stability index were investigated.It is found that the stochastic stability of the system can be strengthened by the bounded noise.