The Survival Analysis Of Species In A Polluted Environment

So far, the persistence and extinction and so on for the dynamic model of species in apolluted environment have gotten a lot of results. To examine these dynamics model notonly has a wide range of theoretical biology, but also has important practical applicationvalue. This paper will discuss the persistent and extinction of the single and two speciesmodels respectively, and also study the existence and the globally asymptotical stability ofperiodic solution for our species systems. The main contents are summarized as follows:In the first section, we first introduce the biology background of the species systems ina polluted environment. Then present a variety of species models in a polluted environment.Finally, we will give this article's research content and organizational structure.In the second section, we study the persistence and extinction of a single species modelwith pulse input of environmental toxin. Using the compare method we get the su?cientconditions under which the system in persist and extinct. what's more, by using Floquettheorem we get the asymptotic stability of the zero periodic solution, using the fixed pointtheorem of Brower we obtain the existence of nonnegative period solution for our system,and we deduce the globally asymptotical stability of the nonnegative period solution byconsidering a Liapunov function.In the third section, using the same method we study the persistence and extinctionof a non autonomous single species model in a polluted environment, and get the su?cientconditions under which the system is uniformly strong (weak) persistent. When the systemis a periodic system, using the continuation theorem of coincidence degree we establisha sufficient criteria for the existence of the positive periodic solution, and also we use aLiapunov function to get the globally asymptotical stability of the positive period solution.In the fourth section, we further study the prey-predator dynamic systems in a pol-luted environment. We get the su?cient and necessary conditions for the extinction andpersistence of the system. By using Floquet theorem we get the asymptotic stability ofthe nonnegative periodic solution, and using a Liapunov function we deduce that when the period solution is asymptotically stable it is also globally asymptotically stable.In addition, the application of theorem of this paper give the conclusions of all give thecorresponding examples and numerical simulation.