Dynamical Behaviors Of Impulsive Differential Systems

Ecological models are important in biomathematics, based on the theorem of Impulsive Differential System, this paper studies dynamics of ecological models with impulsive effect, it is arranged as follows:Chapter 1 gives the background of the research and the preliminary knowledge and introduces the main work of this paper.Chapter 2 is on an eco-epidemic model with impulsively releasing, by using comparison theory and Floquet theorem, the conditions of the global asymptotic stability of the extinction periodic solution and the permanence of the system are given, and numerical simulation is also used to verify the research.Chapter 3 is on an epidemic model with birth pulse and pulse vaccination, by building discrete map and the theory of bifurcation, the stability of the infection-free periodic solution, the bifurcation of the nontrivial periodic solution and relevant numerical simulation are given.Chapter 4 is on an eco-epidemic model with impulsively biological control effect (impulsive harvesting), by using Floquet theorem and coincidence degree theory, the conditions of the local asymptotic stability of infection-free periodic solution and the existence of T-periodic solution are given, and numerical simulation is also used to verify the research.Chapter 5 summarizes the work of this paper and envisages the research in the future.