Dynamic Analysis Of Two Kinds Of Predator-prey Models With Stochastic Disturbance

Stochastic biological mathematical model is one of the hot topics of current research.In nature,ecosystem will inevitably be affected by various environmental noise.Mathematical models with environmental noises can usually be described by stochastic differential equations,which can more accurately reflect the changes of the ecosystem.In this paper,the dynamic behavior of two kinds of stochastic predator-prey models is studied.Firstly,a stochastic predator-prey model with Markov transformation and different functional responses is studied.Secondly,a stochastic Lotka-Volterra predator-prey model with time delay and feedback control is studied.Through theoretical proof,the sufficient conditions for the persistence and extinction of the system are obtained,and the theoretical proof is veri fied by a series of numerical simulations.In the first chapter,a brief introduction is made to the biomathematics,the research background and current situation of two kinds of stochastic predator-prey models are introduced.Then introduce the knowledge of Markov chain,stochastic process,stochastic calculus and related important inequalities.In the second chapter,we construct a stochastic population model in which predators compete with each other and have different functional responses.Considering the influence of white noise and electrical noise disturbance on the model,the dynamic behavior of the system is studied.Using the Chebyshev inequality,the boundedness of the system is discussed.By constructing appropriate Lyapunov function and using Ito formula,the conditions of stochastic persistence and extinction of the system are obtained.Furthermore,the asymptotic property of the system is studied by means of exponential martingale inequality.In the third chapter,a class of stochastic Lotka-Volterra prey-predator model with discrete delays and feedback control is studied.First,the existence and uniqueness of global positive solutions are proved.Secondly,the asymptotic behavior of the stochastic system at the positive equilibrium point of the corresponding deterministic model is studied.The sufficient conditions for system persistence and extinction are discussed.Finally,the theoretical results are numerically simulated.The biological significance of the theoretical results shows that the population can not resist the large disturbance of the external environment and become extinct.When the random disturbance intensity is small,the number of predators can be controlled within a certain range by rational use of feedback control to maintain the sustainable survival of the population system.In the fourth chapter,The work of the full text is summarized and forecasted.