The Dynamic Behavior Of Stochastic Species Models

Population ecology originated in the demographic, applied entomology and aquatic resources through practice, which is a science to study of population dynamic interaction relationship of science and the environment. The research method is through the mathematical model to understand, explain, predict the change rule of the ecological society which could help us to protect our survival on earth species in nature. Early on, scholars studied the population ecological system through the establishment of a deterministic system. Lotka-Volterra is a model based on facilitating the study of population ecology system, the model made epochal significance for the whole ecological theory. It opened a new chapter to ecological studies. Since then, ecosystem ecology has a rapid development and became a hot issue in academic research. Now, not only in the aspect of pure theory but also research ways of population ecology play a significant role in the whole development of ecology.In this paper, we consider the parameters in the population models with stochastic perturbation and study their dynamic behaviors. In the second part, we mainly discuss the multi-competitive system, predator-prey system with stochastic perturbation which are and we show there exist unique positive solutions of the stochastic systems. then, when the intensity of the white noise is small, we get the conclusion that the random systems have stationary distribution and ergodicity by Has’minskii method. How-ever, when the intensity of the white noise is large, we investigate that all species extinct or part of the population extinct, some groups tend to be stable. Finally, we use Milstein strict calculation method of stochastic differential equation to do numerical simulation and give the detailed numerical simulation of the image.In the third part, we mainly study the persistence and non-persistence of the three species food chain random system. We discuss the dynamic behavior of food chain model and its corresponding delay form with random disturbance which are andWe show there exist unique positive solutions of the time-delay system and non time-delay stochastic system and discuss the P moment boundedness. We discuss the permanence and extinction of the system in the sense of time average and verify the conclusion through the method of numerical simulation.In the fourth part, we mainly discuss the dynamic behavior of the three species Holling II food chain random system which isFirst, the balance and stability of corresponding deterministic system is given. Then, using Lyapunov theorem and Ito’s formula we prove the existence and uniqueness of solution for stochastic system. Finally, we discuss the progressive behavior of stochastic system around the deterministic system equilibrium point and use the numerical simulation of the traditional method to validate the conclu-sion.All in all, in this paper, we point out that the stochastic systems imiate the corresponding deterministic systems if the white noise is small; while if the white noise is large, the stochastic systems have more different properties, such as the persistence, etc. In the reality, the strong white noise can be understood as a sudden extreme weather, etc.