| The plankton model is an important topic in the study of marine biodynamics.The researches mainly are analysis and exploration of the plankton model in the influence of single factors at present.However,there are many factors affecting the interaction among plankton in nature,such as nutrients,delay,spatial diffusion,etc.Therefore,this paper mainly establishes plankton model considering multiple factors,and studies its stability,bifurcations and control problems.In Chapter 2,a Holling type-? nutrient-plankton model with time delay and linear plankton harvesting is investigated.Firstly,the bound,the existence of all equilibria and their local stability of model without time delay are given.Then,when the system contains the time delay,regarding time delay as bifurcation parameter,such system around the interior equilibrium loses its local stability,and Hopf bifurcation occurs when time delay crosses its critical value.In addition,the properties of the Hopf bifurcation are investigated based on normal form theory and center manifold theorem.What's more,the global continuation of the local Hopf bifurcation is discussed by using a global Hopf bifurcation result.Furthermore,the optimal harvesting is obtained by the Pontryagin's Maximum Principle.Finally,some numerical simulations are given to confirm our theoretical analysis by using Matlab.In Chapter 3,a delayed diffusive phytoplankton-zooplankton model with BeddingtonDeAngelis functional response and toxins is investigated.Firstly,existence of equilibria of this system are solved,and the global asymptotic stability of the zooplankton free equilibrium is obtained by the iterative method.Then,the local stability of the coexistent equilibrium and existence of Hopf bifurcation are discussed.In addition,the properties of the Hopf bifurcation are studied based on the center manifold and normal form theory for partial differential equations.Finally,some numerical simulations are also carried out to confirm our theoretical analysis. |
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