Research On The Stability Of Stochastic Predator-prey Systems With Impulsive

With the development of society,people's attention has been paid to ecological and environmental issues.For human beings,it is very important to better know the dynamics of populations,predict the developments of species and control the system to be a stable state through man-made adjustment.Based on the real world,three types of stochastic predator-prey systems with impulsive effects,stochastic disturbance and some different kinds of functional responses are established in this paper.By use of It(?) formula,stochastic differential equation comparison theorem,Lyapunov functional theory and some analytical techniques,the dynamic properties of above systems are discussed,and finally the conclusions obtained are verified by numerical simulation.The article mainly consists of the following contents:Some related biological background,research status and main works of the impulsive and stochastic ecosystem are introduced in the first chapter.The main definitions and lemmas of this article are put forward to pave the way for the proof of our results later in the second chapter.In Chapter 3,a modified Leslie-Gower and Holling-IV random predator-prey system with Levy noise and pulse toxin input is established.Using It(?) formula with jumps,random differential equation comparison theorem,Chebyshev inequality and ergodic method,we study the distribution stability of this system.By using the strong law of large numbers,random comparison theorem,we obtain the sufficient conditions of the persistence and extinction for predation and prey.Finally,the theoretical results are verified by numerical simulation.Simulations imply that Levy noise has a strong influence on the dynamics of the predator-prey system.In Chapter 4,considering the impact of population capture,we build a Leslie-Gower Holling-II stochastic predator-prey system on the basis of Chapter 3.Using stochastic system theory and Cheby-shev's inequality,we establish the sufficient conditions of extinction and persistence of each species,and the stable in distribution of this system,then we investigate the optimal capture strategy of all species.Finally,numerical simulation is performed to verify the main results and explore the dynamic behavior of the system.In Chapter 5,a class of non-autonomous Holling-Leslie predator-prey system with random distur-bance and impulsive disturbance is proposed.By constructing a suitable Lyapunov functional and using Khasminskii theory,the existence of T-periodic solutions,the extinction and persistence of each popula-tion,and the global attractiveness of the system are studied.Finally,some numerical simulation diagrams are given to verify our theoretical results.The results obtained in this article enrich the theory of impulsive stochastic ecosystems,reveal the effects of impulsive and random disturbances on the dynamics,and provide a certain theoretical basis for the development of ecosystem resources.