Stability Analysis Of Two Kinds Of Discrete Predatorprey Models With Impulse

In the ecosystem,many phenomena of life and the intervention and control of people are not continuous process.It is not possible to use a differential equation or a difference equation in the description,but to use the impulse equation to describe it.The impulsive equation can describe the instantaneous burst phenomenon better.It can not only express the effect of the instantaneous burst on the system state,but also can reflect the changing regulation of the object more accurately.In this paper,we mainly study the dynamical behaviors of two kinds of discrete impulsive biological models,analyze the permanently and stability of the predatorprey model with the influence of impulsive,and the numerical simulation is carried out.In the first chapter,we mainly introduce the historical background and significance of the subject,the development and research status of the impulse equation,Holling II functional response function,delay equation and impulsive equation in the field of mathematical biology are introduced..In the second chapter,we use the Euler method to construct a discrete predator-prey model with impulse and Holling II function.Through the spraying of pesticides and releasing natural enemies to force pulse,using the Floquet theorem to prove the existence of periodic solutions of pest extinction,and point out when the impulsive period is less than some critical value,pest eradication periodic solution is globally asymptotically stable.It is proved that the discrete system is permanent when the impulse period is greater than a critical value.The results of numerical tests are given and the results are verified.In the third chapter,we use the Euler method to construct a non autonomous discrete predator-prey model with impulsive and multi-delay.In this paper,we mainly study the influence of the at the time lag of the changes on the stability of the discrete model,through the analytical method in certain conditions we also prove that the system is permanent,by constructing a Lyapunov function we prove that the system is asymptotically stable under certain conditions.The results of numerical tests are given and the results are verified.