Stochastic Stability Analysis Of Three Types Of Mathematical Ecology Models

Because of stochastic differential equation models more realistic and attracted wide attention of many scholars, so this area has been further developed. For a discussion of public health and protection of natural resources, the paper describes the three types of ecological models, and analyze the stochastic stability.At first, we discuss the drinking model with random perturbation, allowing ran-dom fluctuation around the endemic equilibrium of deterministic drinking model. By constructing Lyapunov function, we obtain the sufficient conditions of random perturbation, which can guarantee the stochastic asymptotical stability of the en-demic equilibrium.Secondly, in this paper, we introduce a drinking model which put the drinkers(A) into two types(A1and A2), A1represents those who do not admit alcohol problems, A2denotes those who admit the problems. The system takes the random perturba-tions into account. By employing direct Lyapunov method and using Ito’s formula, we obtain a sufficient condition for the stochastic asymptotic stability in the large of the endemic equilibrium.Finally, research two kinds of harvesting model with random perturbations, a detailed analysis of the two models of random perturbations around equilibrium sit-uation. Through the establishment of Lyapunov function, stochastic global stability is proved, and we get the stability conditions...