Analysis Of The Epidemic In A Predator-prey System With Refuge Under The Impact Of Odor

The impacts of odor by predator is that the odor of predator can reduce the population reproduction rate of prey.Nowadays,in order to protect the endangered species,establishing nature reserves has become the most effective way.However,because of excessive protection of person or lack of natural enemies,the quantity of some species is becoming more and more,exceed the load capacity of ecological system.Take appropriate odor to control the number of population is good for maintain the ecological balance.So,study the model in a predator-prey system with refuge under the impact of odor has very important practical significance.Based on the population age structure,the function response in prey-predator or others will have important effects on predator-prey system,using the population dynamics,the qualitative theory of differential equations to set Mathematical madel,having a in-depth analysis.At first,this papere analysis of the model in a predator-prey system with refuge under the impact of odor,proved the existence of the equilibrium point and local stability.Using the Dulac-Bendixson theorem proved the global stability of co-existing equilibrium point.At last,numerical simulations are performed to illustrate and verify the conclusions.Secondly,we present a model with Logistic growth and Holling type-II response.showed all solutions of system are bounded and the existence condition of the equilibrium point,we get stability of co-existing equlibrium for the model by mean of suitable Lyapunov functions.Finally,we establish a model with refuge and stage structure.Whilst the dynamic behaviors of model is investigated,proved the existence of the equilibrium point,using the hurwitz stability criterion proved the local stability.