Analysis Of Plankton Growth Model With Delay

Plankton refers to drifting creatures that live in water without effective movement,most of them float on the surface of the aquatic environment.Plankton is the producer and primary consumer of aquatic ecosystem and plays an important role in material circulation and energy flow.In resent years,many studies have a strong interest in the analysis of mathematical models.In the study,they increasingly take into account the factors that affect the interaction of plankton,making the model closer to reality.Time delay is one of the important factors in many influential factors.In this paper,three models are considered,and the generality is that the release of phytoplankton toxin is considered in all models.Furthermore,the third mode adds nutrient to the delay factors,and the plankton system with nutrient cycling and time delay is studied.Throng the study of the existence,positivity,boundedness of solutions and the existence,stability of positive equilibrium,we have come to some conclusions about the significance on plankton.The main contents of this paper can be summarized as follows:In section 1,we introduced the research background,purpose and significance of plankton interaction model,and present the current research situation and results of the plankton model.The structure of this article is also showed in the last part.In section 2,we studied a toxic producing phytoplankton-zooplankton interaction model with hunting delay.Firstly,positivity and boundedness of solutions are given.Then the stability and the occurrence of Hopf bifurcation of the coexistence interior equilibrium are investigated.Finally we verify the analytical findings by numerical simulation.In section 3,we analysed a toxic producing phytoplankton-zooplankton interaction model with gestation delay and maturity delay.Firstly,the existence of the equilibrium point of the model is discussed mainly.Then the local asymptotic stability of the equilibrium and conditions of Hopf bifurcation existence are studied.Last,some numerical simulations are executed to validate the analytical findings.In section 4,we discussed a toxic producing phytoplankton-zooplankton interaction model with nutrient cycling and time delay.We established Lyapunov function to research the global asymptotic stability of the equilibrium primarily.