Dynamical Analysis Of Phytoplankton-Zooplankton Model

This paper considers the nutrient with cycling and phytoplankton interaction model and phytoplankton with discharging toxins and zooplankton interaction model. The boundedness and negative of the solutions of models are given, discussed the existence, stability, durability and Hopf branch of the boundary equilibrium and the positive equi-librium point. Using the numerical mode further reveals complex Dynamic behavior of the systems.The main contents in this paper can be summarized as follows:The first section is introduction, in which we present research background, purpose and significance of the model of phytoplankton-zooplankton-nutrient interaction. And then the research status and results of model are given.In Section2, Firstly, we consider the phytoplankton and nutrient with cycling in-teraction model, Response function of nutritional intake and growth response function have the general form. The Existence and stability of boundary equilibrium and positive equilibrium of the model are discussed. Secondly, we consider the phytoplankton and nu-trient with cycling interaction model with delay, we discussed the possible occurrence of branches and stable switch. Using numerical simulation Further illustrate the complexity of the dynamic behavior of the model.In Section3, A dynamical model for toxin producing phytoplankton with time de-lay (based on phytoplankton release toxins must reach a certain age) and zooplankton has been formulated and analyzed, Investigate the existence, stability and bifurcation of equilibrium point, Determined the range of Delays τ to appearance of Hopf-branch and periodic solutions. Using Lypunov-Lasalle invariance principle proved the persistence of the system. The complex dynamical behavior of the system was observed by numerical simulation. In Section4, Conclusion and discussion are given.