Dynamic Analysis Of Two Kinds Of Predator-Prey Models With Impulsive Diffusion

In this paper,we study the global asymptotic stability of the positive equilibrium by constructing Liapunov function according to the Lotka-Volterra predator-prey model.The analysis shows that the related parameters can be controlled to realize the persistent coexistence of the prey and the predator.On the basis of this model,we introduce the alien population,and establish a nonlinear impulsive intrusion predator-prey model to analyze the relationship between species.In addition,the impulsive differential system with Allee effect is studied to analyze the coexistence of native species and alien species.The model analysis shows that it is of practical significance to control the biological invasion or introduce alien population.According to the characteristics of the growth stages of alien species,we established the impulsive dynamics model of the alien in Logistic.By using Floquet theorem and comparison theorem,the model investigate the global asymptotic stability of periodic solution,which can be used to provide guidance for the control strategy of biological invasion.According to the conditions of the system,we can get some conditions that the pulse period needs to be satisfied.The pulse period conditions can also be used to introduce new species,to enrich the number of species and achieve the harmonious coexistence of biological diversity.In addition,considering the influence of the Allee effect,a predator-prey model with Allee effect is established.In this model,the conditions for the global asymptotic stability of the prey extinction periodic solution are analyzed.This will provide an important theoretical basis for the management of exotic species with Allee effect,and it can be used as a reference for the decision-making of the relevant management departments.