Permanence For Several Nonlinear Biological Models

Along with the rapid development of social economic activity,because of short-term interests of humanity and lack of awareness of nature,blind predatory economic activity such as large-scale deforestation and reclamation of cultivated land,illegal poaching,non-standard tourism,mining and factories blindly "three wastes" the release and so on,have caused desertification,soil erosion,environmental pollution and the rapid disappearance of species,such as a series of serious consequences. As we know,loss of biodiversity and ecological have damaged to the environment and human's survival.In the process of studying biological extinction,people found that the extinction of many biological processes are habitat broken firstly,species continuous distribution of species fragmented into patches,then patch-by-species extinction,and finally cause the extinction of entire species.The persistent problem of biological species for the differential equations in mathematics is a long-term coexistence of accurate and scientific description.Recently,the delay differential equation in the ecological model widely is applied widely to study the impact of delay on the stability.From some of the model with time delay,we know that the stability will change with the changing time delay and will cause unlimited growth of the system eventually becoming unstable.In addition,the stage-structured population models are widely concerned about the phase structure of the model because of its form different from partial differential equations and more simple,In the second chapter,a class of predator-prey model with Beddington-DeAngelis functional response function and the infinite delay is concerned,necessary and sufficient conditions of permanence are obtained by using the comparison theorem.Impulsive differential equation describes the status of certain sports at fixed or rapidly changing moment.It is widely used in species dynamics,dynamics of infectious diseases, pharmacokinetics,bio-cybernetics,bio-statistics,the number of genetic,chemical reactions and so on.However,the application of impulsive differential equations in Population dynamics and Infectious Diseases remains gaps in study.Therefore, this article in Chapterâ…¢studies a class of impulse prey-predator model with nonmonotonic functional response function of sustainability and obtains the conditons of permanence and the extinction of the model by Using Floquet theorem and small parameter perturbation technique.Infectious diseases have always been against the great enemy of population health,history time and time again on the prevalence of infectious diseases to human,the people's livelihood has brought enormous disaster. So,chapterâ…£of this article constructed a pulsed pest control virus disease model, that is,pest species and pulse are injected through the worm susceptible to achieve the purpose of the eradication of pests.