Stochastic Stability Analysis Of Two Kinds Of Biological Predator-prey Systems

With the rapid economic growth,more and more attention has been paid to the ecological environment problems.Using mathematical modeling as a tool to study the complex problems in biological mathematics and ecology,people have a more comprehensive and profound understanding of the laws of biological development and change,And some more abundant research results have been obtained.However,in previous studies,the deterministic model is the main research object,and can not objectively describe the real ecosystem.In order to build the more practical model,the randomness is introduced into the biological predator system in this paper.Make use of theoretical knowledge of stochastic dynamical systems,stochastic differential equationsa and with the help of constructing appropriate Lyapunov functions and some inequalities,the stability of Two kinds of stochastic biological predator prey system are studied.This main work are as follows:First,we briefly described the research background and significance of biological predator system,as well as the research status of biological population system is introduced,and the stability theory of stochastic dynamical system is introduced.Secondly,the orthogonal polynomial approximation theory is applied to transform the stochastic system.into an equivalent deterministic system.The conditions for maintaining the local asymptotic stability of a biological predator system under the influence of random parameters are studied by Jury criterion.Then the numerical simulation results are carried out by the mathematical software,and the effects of the different statistical parameters and the random strength on the local asymptotic stability of the system are compared and analyzed.Thirdly,by using It(?) formulas and some inequalities theory.We construct the appropriate Lyapunov function.The global asymptotic stability of a kind of biological predator-prey system with Hassell-Varley type functional response under noise excitation is studied.The the existence and uniqueness of the solution and global asymptotic stability of a kind of biological predator-prey system with Hassell-Varleytype functional response under noise excitation is studied.The sufficient conditions for the global asymptotical stability of the nonzero equilibrium point of the system are given.Finally,the correctness of the conclusion is verified by numerical simulation.Finally,in view of the shortcomings of the paper,the future research work is put forward,and the direction and suggestions for further research are given.