Some Research On Behavior Of Dynamics In Plankton Populations

This paper mainly research on behavior of dynamics in plankton populations. The hot topics of continuous dynamical system and impulsive dynamical system are discussed, and a series of important results are obtained.In Chapter 1, the research background and research situation of population dynamical system are introduced, and some important definitions and lemmas are provided, which are theoretical basis for the subsequent chapters.In Chapter 2, the dynamics of a nutrients-phytoplankton system with Holling type II functional response are studied analytically and numerically. Firstly, using the theory of differential equation and population dynamics, the certain conditions for boundedness of solutions and existence and stability of equilibria have been obtained. Then, global stability of equilibria has been proved by constructing the Lyapunov function. Furthermore, the uniform persistence of population has been analyzed. Finally, numerical simulation indicates that the runoff of nitrogen seriously affects the dynamic change trend of system dynamics. These results help us to understand deeply the dynamics behavior of phytoplankton population in the actual aquatic ecosystem.In Chapter 3, the dynamics of a phytoplankton-zooplankton system with impulsive state feedback control and Holling type II functional response are studied in detail. Using the analogue of the Poincaré criterion and a geometric method, the certain conditions for the existence and stability of semi-trivial periodic solution and order-1 periodic solution are obtained. Then, the transcritical bifurcation and the bifurcation of order-1 periodic solution are discussed. Numerical results verify the correctness of the theoretical results, and find the chaos phenomena which is caused by impulsive control. In addition, the largest Lyapunov exponent further verifies the existence of chaotic behavior. These results are useful for studying the mechanism of algal blooms.In Chapter 4, the dynamics of a phytoplankton-zooplankton system with impulsive state feedback control and Holling type I functional response are studied analytically and numerically. Firstly, the existence and stability of semi-trivial periodic solution are proved. Then, in the cases of *x ?h and *x ?h, the existence and stability of order-1 periodic solution are discussed respectively. Finally, numerical simulations verify the correctness of the theoretical results.