Existence And Persistence Of Positive Periodic Solution For System With Beddington-DeAngelis Functional Response And Impulse

In the previous related papers,the Lotka-Volterra model with the traditional Michael-Menten or Holling functional response have already been researched extensively by biologists and mathematicians on stability and existence of periodic solutions of system and they have obtained a lot of research results.Compared to such systems, people found that predators-prey model with the ratio which be put forward by Arditi and Ginzburg will be more coincident with the fact when people describe the impact of behaviour of the Predator upon system(especially as predators have to search for food),and in recent years,about such system and its form of generalization has been widely explored.Although the ratio-dependent model has even richer,more complex,more reasonable dynamic behavior,but their singular act in the low density has aroused the arguement of researchers.Recently, Bedding-ton and DeAngelis introduced another type of functional response (known as Beddington-DeAngelis functional response),which has aroused the interest of many scholars,in predator-prey model. Statistics show that the system with Beddington-DeAngelis functional response is more tallies with actual data in describing some dynamic behavior of ecosystem and simultaneously has overcomed the singular act in low-density state.In the actual process of animal protection,people usually protect wild animals by the diffuse way which make the population of forthcoming extinction migrate the living environment,so diffuse function in different patch environment has aroused more and more people' attention, at the same time,in the protection of wild animals,people usually use the way of artificial feeding,and supply the wild animals by periodic stocking.In this paper,we consider a nonautonomous predator-prey system with Beddington-DeAngelis fuctional responses and stocking rate,it is proved that the system is uniformly persistent under suitable condition.Furthermore,a sufficient condition are established for existence of periodic solution and uniqueness of global asymptotic stability by establishing Liapunov ruction and a example is given to illustrate the feasibility of these conditions. The basic survival relationship between different species can be divided into reciprocal relationship and predation relationship and competition relationship,but the relationship between many species is not single and activities of species is periodic obviously,we consider a nonautonomons multispecies ecological competition-predator system with impulsive effect and Beddington-DeAngelis fuctional responses.A sufficient conditions are established.for existence of periodic solution of the system by using coincidence degree.