The Persistence Of Population Ecological Model In A Polluted Environment

In this thesis,we considered models of several population dynamical systems and dis-cussed their dynamical behaviors by Floquet theory of impulsive diferential equation,Lyapunovfunction,comparison theorem of diferential equation etc,including the existence and unique-ness theory of periodic solutions,the existence and stability of a positive asymptoticallyperiodic solution,the persistence and extinction of the system ect.This paper is composed of four chapters.In Chapter1,we introduce the background and signifcance of population ecologicalmodel,overseas and domestic research status,and some preliminaries have been given.In Chapter2,a stage-structured predator-prey system with Holling type-IV functionalresponse concerning impulsive control strategy is investigated in a polluted environment.Itis proved that there exists a global asymptotical stable periodic solution.Further,sufcientconditions for the permanence of the system are established.In Chapter3,we considered a predator-prey model with disease in the prey.Prey is re-stricted by density and predators mainly prey on infected prey.The local and global stabilityof the system is proved.In Chapter4,a mathematical model for HIV-1infection with intracellular delay is for-mulated in a polluted environment.We obtain a necessary and sufcient condition for theglobal stability of the infection-free equilibrium and give some sufcient conditions for thelocal stability of the infected equilibrium.