The Dynamical Research Of An Age-structured Aquatic Plankton Model

In this paper,an age-structured aquatic ecological model is proposed to study the effect of the maturation age of zooplankton.After theoretical analysis and numerical simulations,the sufficient conditions of the local stability of the equilibrium and Hopf bifurcation are obtained.The result shows that the maturation age of zooplankton can influence the stability of the equilibrium and give rise to the emergence of oscillations.In chapter 1,the introduction part gives an outline of the research background and the present research situations.Besides,some basic definitions and primary lemmas are given.In chapter 2,a phytoplankton-zooplankton model with harvesting effect is established.Based on theoretical analysis,the global stability of the trivial equilibrium,boundary equilibrium and positive equilibrium are discussed.Numerical simulations are given under different harvesting conditions and the simulation results verify the theoretical results.In chapter 3,based on the model and the results obtained in chapter2,a phytoplankton-zooplankton model with age structure and time delay is proposed to study the effect of time delay and the maturation age of zooplankton.The uniqueness and stability of the positive steady state and the Hopf bifurcation are discussed.The result shows that the maturation age of zooplankton or time delay can influence the stability of the positive equilibrium.In chapter 4,according to the above conclusion,an age-structured nutrient-phytoplankton-zooplankton model is studied.After theoretical analysis,the result shows that the maturation age of zooplankton can induce Hopf bifurcation at the equilibrium and cause oscillations of the nutrient-phytoplankton-zooplankton model.Finally,simulations are givenand they are in accordance with the theoretical results.