The Study Of Dynamics On Stochastic Population Models With "Rock-paper-scissors" Effect

In recent years,with the deepening of the study population model and the expansion of rock-paper-scissors theory,the research on population models with“rock-paper-scissors” effect is becoming more and more popular.In the real world,the survival and development of the population are inevitably influenced by environment noise,so it is necessary to consider white noise in the establishment of population models.In this thesis,some theories of stochastic differential equations and rock-paper-scissors are used to establish stochastic population models with“rock-paper-scissors” effect.Next,the dynamical properties of the three-dimensional model and the generalized four-dimensional model are studied.Finally,the numerical simulation verified the result of the theory.The main contents are as follows:At first we introduce the research background and significance,the research status as well as the main works that we have done in this thesis,and give some symbols,definitions and theorems.Then a three-dimensional stochastic population model with "rock-paper-scissors" effect is established and investigated.By constructing suitable Lyapunov function and using the ?Ito formula,we investigate the property of solution such as existence,uniqueness and stochastic boundedness,give sufficient conditions for global asymptotic stability of the system,and further study the long time behavior of the system.Finally,the numerical simulations are given to verify the correctness of the conclusion.At last,we establish and investigate the generalized four-dimensional model depend on the three-dimensional model in the third chapter through relevant literature.Using the It(?) formula and some of the inequalities technique and constructing appropriate Lyapunov function,the property of solution and sufficient conditions which guarantee the stochastic permanence and extinction of the four-dimension stochastic system are obtained.Besides,corresponding numerical simulations are presented to certify the availability of the main results.