The Survival Analysis Based On Mathematics Theory Of Some Stochastic Ecological Models

Sustainable development of biological population is one of the key problems in the world in recent years. Survival analysis of biological population have become more and more prominent in academia at home and abroad. Because population dynamics is in-evitably affected by all kinds of environmental noises, impulsive perturbation and time delay in the real world, we established five kinds of ecological models. The main aim of our work is to investigate the survival analysis of them and the main content in detail are as follows:1. A stochastic nonautonomous logistic model driven by Brownian motion is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersis-tence in the mean, weak persistence, stochastic permanence and global asymptotic stabil-ity. Meanwhile, the threshold between weak persistence and extinction is obtained, our results demonstrate that the stochastic perturbation is disadvantageous of nonpersistence in the mean, weak persistence and stability of the population.2. With space Cg as phase space, we investigated two kinds of stochastic logistic models with infinite delay. For the two models, sufficient conditions for extinction and various persistences are established, respectively. The threshold between weak persistence and extinction is obtained. The results implies that, firstly, different stochastic perturbation on parameters have different effects on the persistence and extinction of the population mod-el; secondly, the delays has no impact on the persistence and extinction of the stochastic model in autonomous case. Numerical simulink graphics illustrate our main results.3. We considers a impulsive stochastic logistic model with infinite delay. Firstly, with s-pace Cg as phase space, the definition of the solution to an impulsive stochastic functional differential equation is established. Second, we establish the sufficient conditions for ex-tinction and various persistences. The threshold between weak persistence and extinction is discussed. Then, we can find that the impulse does not affect the properties including extinction, nonpersistence in the mean and weak persistence if the impulsive perturba-tions are bounded and some changes significantly if not. Finally, numerical simulations are introduced to support the theoretical analysis results.4. A stochastic Gilpin-Ayala model driven by Brownian motion and Levy process. We establish the sufficient conditions for extinction and various persistences. The threshold between weak persistence and extinction is investigated. The results shows that the jump process is disadvantageous of persistence and force the population to be extinct, which conforms to biological significance simulated. The simulations also conform our analyti-cal results.5.(1)A stochastic delay logistic model with Levy jumps. Sufficient and necessary con-ditions for extinction and stochastic permanence of the model are obtained. The results show that the jump process is unfavourable to persistence.(2)A stochastic delay logistic model with general Levy jumps. Sufficient and necessary conditions for extinction and stochastic permanence of the model are given. The result-s show that its effect on permanence depends on jump-diffusion coefficient. When the jump-diffusion coefficient is bigger than zero, Levy noises benefit permanence. When the jump-diffusion coefficient is less than zero, Levy noises was not favourable to perma-nence.