Study On The Population Ecology Models With Time Delay And Impulsive Effect

Population biology is a very important branch of biomathematics. Based on classic ordinary differential equation models, the population biology models with time delay and impulsive have been considered. This paper organized as follows:In the first chapter, the development population biology systems are given, and the major work in this paper is also introduced.In the second chapter, a class of food chain system with stage structure is studied. The existence and boundedness of the positive solutions of the system is investigated. The stability of the equilibrium is studied by analyzing the characteristic equations. By using numerical simulations showing system periodic oscillation, quasi-periodic oscillation, chaos and so on complex dynamics behaviors, and has analyzed the stage structure to the system complex behavior influence.In the third chapter, a two-prey one-predator system with delays is studied. The stability of the equilibrium points is discussed. By applying the theorem of Hopf bifurcation, the characteristic equations of the positive equilibrium is analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation is given. Numerical simulations are carried out to illustrate the local asymptotically stable (LAS) and Hopf bifurcation periodic solution of the system positive equilibrium. It can be concluded that this system has periodic phenomena and the three populations can be coexistence under such conditions.In the last chapter, an Ivlev-type two-prey one-predator system concerning integrated pest management (IPM) is studied. The sufficient conditions for prey-eradication periodic solution and permanence of the system are obtained by using Floquet's theorem and comparison theorem of impulsive differential equation. Numerical results show that the system considered has rich dynamic behaviors, including periodic-doubling cascade, chaos, attractor crisis, non-unique dynamics etc.