Response And Reliability Of Some Classes Of Nonlinear Systems Under Poisson White Noise Excitation

The response and reliability of several classes of nonlinear systems to Poisson white noises are investigated in the present dissertation.In chapter 2, the approximate stationary probability density function and mean square value for the response of multi-degree-of-freedom dissipated Hamil-tonian systems to Poisson white noises are obtained by solving the fourth-order generalized Fokker-Planck-Kolmogorov equation using perturbation approach. In comparison with the Gaussian excitation case, it is shown that the non-Gaussian behavior depends on the product of the mean arrival rate of the impulses and the relaxation time of the oscillator.In chapter 3, 2-degree-of-freedom elastic vibro-impact systems under external and parametric Poisson white noise excitations, respectively, are investigated. The solution of the generalized FPK equation is obtained via perturbation approach. A conforming coefficient is introduced to overcome the incompatible characteristics of PDF caused by piecewise property of the contact force. The approximate probability density function of stationary response is obtained and some useful conclusions are made. The stochastic jump and its bifurcation of vibro-impact system to bounded noise are observed.In chapter 4, a stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of discrete random fluctuations is modeled as Poisson white noise. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at the state of statistical quasi-stationary. The time evolution of the population densities is studied and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from the Gaussian-type one, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations. The work reported may make the picture more clearly for prey-predator systems under discrete fluctuations.The validity of the proposed approaches is confirmed by using the results obtained from Monte Carlo simulations.