The Study Of Population Dynamical System With Time Delay And Impulsive Effect

It is well-known that many real world phenomena and human activities in population dynamics do have tine delay and impulsive effects. In this paper, the population dynamics models with impulsive and time delay on the base of traditional differential model have been considered. This paper arranged as follows:In Chapter 1, the background of the research is given, and the major work of this paper is introduced.In Chapter 2, a class of predator-prey system with discrete and distributed delays is studied. Some sufficient conditions to ensure that the equilibrium of system is asymptotically stable and the Hopf bifurcation exists near the equilibrium are derived. Some explicit formulae for determining the direction, the stability and periodic of the Hopf bifurcation periodic solutions are obtained by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are given.In Chapter 3, a delayed predator-prey system with stage-structured for predator and continuous harvesting on mature predator and impulsive stocking prey is discussed. Applying the theory of delay differential equation and the comparison theorem of impulsive differential equation, we obtain the sufficient conditions of the global attractiveness of predator extinction periodic solution and the permanence of the system, and numerical simulations verify the theoretical results.In Chapter 4, we investigate a predator-prey system with prey impulsively diffusion between two patches. Using the stroboscopic map of the discrete dynamical system, we obtain predator-extinction periodic solution of the system and the globally attractive condition; By the theory of impulsive differential equation, we also obtain the permanent condition of the system and the condition of one patch predator extinction and the other patch two populations coexistence; Furthermore, we give numerical analysis to confirm our theoretical results.