Studies On Effect Of Delay On Phytoplankton Population Dynamics In Water Eutrophication

In recent years,eutrophication has been becoming more and more serious in the oceans,lakes and reservoirs,and then phytoplankton bloom and red tide occur frequently.Based on this,this paper studies the effect of delay on phytoplankton population dynamics in the water eutrophication,and focuses on revealing the dynamic mechanism of phytoplankton growth.Dynamics of a nitrogen-phosphorus-phytoplankton ecological model with delay are studied.The main purpose is to explore how delay affects the specific dynamic behavior of the model.Boundedness and stability of the equilibrium are investigated using differential equation theory.Threshold conditions for the existence of Hopf bifurcation are derived.Furthermore,by center manifold theorem and normal form theory,the direction of Hopf bifurcation and stability of periodic solution are analyzed.Additionally,numerical simulation is performed to further study dynamics in model,which shows that delay plays an important role in nutrient-phytoplankton dynamics.Based upon model in Chapter 2,a nitrogen-phosphorusphytoplankton ecological model with two delays is proposed in Chapter 3.The effect of different delays on the stability of the positive equilibrium and the existence of Hopf bifurcation are studied.Locally asymptotic stability of the positive equilibrium and threshold conditions for the occurrence of Hopf bifurcation are theoretically derived under five different cases respectively.Numerical simulation reveals the evolution process of dynamic behavior such as steady-state switching and Hopf bifurcation,and further indicates the effect of two delays on the dynamic behavior of the model.Finally,the dynamics of a nutrient-phosphorus-phytoplankton ecological model with harvest and two delays are studied.The main purpose is to study the effect of harvest and different delays on the stability of the positive equilibrium and the existence of Hopf bifurcation.Locally asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation are discussed theoretically and numerically.In addition,the effect of harvest on the dynamic behavior of the model is studied as well.Based on theoretical results,a series of numerical simulations are carried out,which show that both harvest and delay can influence dynamics in model remarkably.