Some Dynamical Research Of Eutrophication In Subtropical Waters

Population dynamics is one of the most classic areas of Mathematical Biology. It has always been a hot spot of research at home and abroad. This paper mainly discusses the effect of population dynamics by advection, diffusion and delay.In Chapter 1,the research backgrounds and research status of population dynamics are introduced, and some basic concepts and lemma are also given, which provides a theoretical basis for the subsequent part.In Chapter 2, spatiotemporal dynamics in a diffusive and advection population ecology system are discussed. Firstly, based on the theory of water ecology, we construct a nutrient-phytoplankton system. Secondly, based on stability analysis theory of dynamics, the stability of equilibrium are analyzed in the system, then we derive the critical conditions for Turing instability of the system. Finally, the patterns which are affected by diffusion and advection are plotted by dynamics simulation in the end, it also verify the validity of theoretical analysis.In Chapter 3, the dynamical behavior of a population ecology system with delay effect are studied. Firstly, we built a nutrient-phytoplankton system with the effect of time delay. Then, we discuss the existence of equilibrium, local stability and the key conditions of the Hopf bifurcation occur. Through the center manifold theory, the direction and stability of Hopf bifurcation are confirmed. Finally, through simulation, the results reveal the delay effect have a vital impact on dynamic behavior and characteristic of the system.In Chapter 4, the effect of alternative prey and delay are researched. We build a delayed phytoplankton-zooplankton system with alternative prey. Through the stability analysis of equilibria, we concentrate on the existence and direction of Hopf bifurcation and obtain some better theory results, and the results are verified through computer simulations.