Abstract: By using Monte Carlo Method, the characteristics of bistable dynamics system under the influence of periode and noise force are analyzed. The period non-stationary probability and the joint probability distribution for the system are acquired. Some topological relations among them and the force field and potential, the hole near the saddle point and force zero-point, and the "time bifurcation" are found. The jump characteristic and the signal intensity changing with parameter arealso discussed.

Key words: Monte Carlo method, Probability flow, joint probability distribution, Fokker-Plank equation (FPE), stochastic differential equation, bifurcation, hole, jump, non-autonomous nonlinear stochastic system (NAMLSS)