Dynamic Analysis Of Predator And Prey Problems

Population ecology is a subject that describes the relationship between pop-ulation and environment or the interaction between populations.Many biologists and mathematicians will establish the relationship between population and envi-ronment and population into the mathematical model used to describe and predict the development of species,and through human action to regulate and control the survival and development of the population,that made the population lasting and stable.This paper mainly analyzes and studies the main dynamical behavior of several nonlinear population system.Considering the Allee effect,capture,ran-dom noise,jumping and other factors on the stability of the system,mainly by constructing Lyapunov functions,using Ito formula and stochastic process theory and other methods to study the dynamic behavior of population system.The main contents of this paper are as follows:1.This paper mainly focuses on the stability of predator-prey model,in which Allee effect is exerted on preys,people's capture of predators and preys in the system.The dynamic behavior of the model is analyzed and the existence and stability of the positive equilibrium point is proved.The correctness of the theoret-ical analysis is verified by numerical simulation.The results show that the system should be reasonable to capture,so as to make the population stable.2.A class of predator-prey model with Holling II functional response of two species predators and one prey relationship is studied,through the analysis of the characteristic equation,Routh-Hurwitz criterion and Lyapunov index calculation,the stability of the equilibrium point of the system uncertainty analysis,further by means of numerical simulation analysis of the stability of the system.3.Stochastic cooperative predator-prey system with Holling II functional re-sponse is studied.Our results show that there exists a unique positive solution to the system for any positive initial value,and the positive solution is stochastically bounded.Moreover,under some conditions,we analyze global asymptotic stability of the positive solutions.With small environmental noises,the stochastic system is getting more similar to the corresponding deterministic system.Neither of the species in the system will die out.Thus considering the random environment is very necessary.In each section,simulations are carried out to conform to our conclusions.