Analysis On Dynamics Of A General Non-autonomous Lotka-Volterra Model With Delays

Stochastic factors widely exist in natural science, social science and engineering science in many fields. It will bring great changes to human life if we can use or avoid stochastic factors effectively. In recent years, deterministic population systems have received great attention and have been studied extensively. However, population dynamics in the real world is inevitably affected by environmental noise. So it is im-portant to study stochastic population systems to reveal the effect of the environmental noise on population systems. In recent years, with the rapid development of stochastic differential equations, more and more scholars are engaged in the research of stochastic nonlinear systems. Compared with ordinary differential equations, stochastic differen-tial equations can more truly and accurately describe the dynamic character of the sys-tems. At present, more researches of the stochastic population models have been done and got many interesting results. But there are few people studying the persistence and extinction of the stochastic population models, and the research of the stochastic popu-lation models with time delays and impulsive perturbations is lacking. In view of this, the main work is as follows:1. The dynamics of a general non-autonomous n-species Lotka-Volterra model with delays and stochastic perturbation is investigated. This paper establishes the suffi-cient conditions for the uniqueness and existence of the global positive solution. More-over, sufficient conditions for extinction, non-persistence in the mean, weak persis-tence and stochastic permanence are established. The critical value between persistence and extinction is obtained. The influences of the stochastic noises to the properties of the stochastic model are discussed. Finally, numerical simulations are given to support the theoretical analysis results.2. The dynamics of a general non-autonomous n-species Lotka-Volterra model with delays, stochastic perturbation and impulsive perturbations is investigated. The dynamics properties of the solution have been researched, including the uniqueness and existence of the global positive solution, extinction, non-persistence in the mean, weak persistence and stochastic permanence. The critical value between persistence and extinction is obtained. The influences of the stochastic noises and the impulsive perturbations to the properties of the stochastic population model are discussed. Finally, numerical simulations are given to support the theoretical analysis results.