Dynamic Behavior Of Phytoplankton-zooplankton Model

Plankton is a microscopic organism that floats freely with oceanic currents and in other bodies of water.They are made up of tiny plants and tiny animals,phytoplankton is the main producers in the plankton community.They are not the base of the oceanic food web but to translate energy,mineral chemistry into carbohydrate.Zooplankton are the animal forms that eat other plankton in the microbial community.In recent years,the dynamic behaviors of zooplankton-phytoplankton have been discussed by many authors,such as stability of equilibria,Hopf bifurcation,global stability and so on.Yet,seasonality and periodicity are also essential for the growth of plankton population,therefore,it is meaningful to consider the non-autonomous phytoplankton-zooplankton model.The work mainly discussed in the following two aspects: On a one-phytoplankton two-zooplankton model with harvesting and a non-autonomous phytoplankton-zooplankton model.This work mainly discussed the positivity,boundedness and Hopf bifurcation of the solution.The main contents of this paper can be summarized as follows:The first content is introduction,in which we present research background,purpose and significance of the phytoplankton-zooplankton model,given the phytoplanktonzooplankton model research present situation and the results.Finally the organization of this paper is presented.In section 2,we mainly discussed the positively,boundedness of the solution and existence of nonnegative equilibria of a phytoplankton-zooplankton model with delay.By using Routh-Hurwite criterion and the Lyapunov-LaSalle's invariance principe,we get the sufficient condition for the model of local and global stability of the interior equilibria.Finally,provides some Hopf bifurcation analysis on the system with delay.In section 3,we give the dynamical behaviors of a non-autonomous phytoplanktonzooplankton system.We discussed the permanence and uniqueness of positive periodic solution of the system,and given a sufficient condition for global attractiveness of the periodic solution by constructing a suitable Lyapunov function.