The Analysis Of A Population Model With Nonlinear Birth Rate And Stage- Structure

In this paper, there are three chapters. The preface is in chapter 1, we introduce some knowledge of biology mathematics and the main work.In Chapter 2, we study a Single Species Model with Three Stage Structure-hatch,immature and mature with mature population harvesting,we obtained sufficient conditions for the extis-tence of globally aymptotically stable positive equilibrium.and the optimal harvesting policy of mature population isconsidered.In Chapter 3, we introduce and study a predator-prey model with nonlinear birth rate and stage-structure. In the first section we deals with the behavior of positive solution to a predator-prey model with nonlinear birth rate and stage-structure,and the solution of this system is bounded. The local stability and global stability of the nonnegative equilibrium is investigated by linearization and Dulac function.In the Second section we introduce and study a predator-prey system of two species with stage structure and time delay is considered. The invariance of non-negativity, nature of the boundary equilibria, permanence and global stability are analyzed. The results show that positive equilibrium is locally asymp totically stable when time delayτis suitable small, while a loss of stability by a Hopf bifurcationcan occur as the delay increase. That is, a family of periodic solutions bifurcates from positive equilibrium asτpasses through the critical valueτ.