First Passage Time Of Two Sorts Of Stochastic Dynamic Systems

Because of the universality in engineering as well as the important value in theoretical research, stochastic dynamic systems draw extensive attentions of engineers and scientists. Compared with response evaluation and stability analysis, the first passage problem of stochastic dynamic systems is less investigated. Considering that first passage problem is one of the most difficult tasks of research on stochastic dynamic systems, this thesis focuses on two sorts of extreme systems, i.e., random walk on complex networks and the first passage time of single degree of freedom inverted pendulum subject to combined high frequency harmonic excitation and stochastic excitation.First passage in complex network systems turns to be the search time of file or data on networks using random walk strategy. The search time from source node set to target node set. search efficiency on directed networks using various random walk strategies and search time on scale free networks with different degree relations are investigated. respectively. To the search problem from a source node set to a target node set. the mean search time is analytically derived from the transfer probability matrix, and the difference of mean search time in nearest coupled networks. small world networks and scale free networks is discussed. To improve search efficiency, no-triangle-loop random walk, no-quadrangle-loop random walk. self-avoiding random walk and path-iteration-avoiding random walk are adopted. The avoiding effect of these strategies on directed networks is illustrated. The unrestricted random walk and preferential-self-avoiding random walk strategies are selected to search file or data on scale free networks with different degree relations. Compare with the networks with no degree relation, search on disassortative networks costs less time while search on assortative networks costs more time.The inverted pendulum, subject to high frequency harmonic excitation on its support, is stable at the upside down position under certain conditions. The research on the probability that the inverted pendulum, which is excited on its support by high frequency harmonic component and Gaussian white noise, exceeds given safe domain is significant. and this is the so-called first-passage problem of stochastic inverted pendulum. The direct motion separation method and stochastic averaging of energy envelop are adopted to deal with the high frequency harmonic excitation and Gaussian white noise, respectively. High frequency harmonic excitation turns to the equivalent stiffness item through direct motion separation. and then the backward Kolmogorov equation which governs the conditional reliability function are derived by using stochastic averaging of energy envelope. Solving this equation with associated boundary conditions yields the conditional reliability function and the conditional probability function of first-passage time. The results obtained agree well with that from Monte-Carlo numerical simulation.