Study On The Stability And Hopf Bifurcation Of Two Plankton Ecological Systems With Double Time Delays

This article mainly studied the stability and Hopf bifurcation of two plankton ecological systems with double time delays.Several relevant problems attracting more and more attention in this field are deeply discussed,and a series of relatively perfect theoretical and simulation results are obtained.In Chapter 1,the backgrounds and research status on population dynamic problems of plankton ecological system with time delay are introduced.It also provides the readers with some preliminaries,including important definitions and lemmas that are frequently used in the following chapters.In Chapter 2,it mainly studied the stability and Hopf bifurcation of the nutrient-plankton system with double time delays.The existence and stability of equilibrium point have been discussed,and the existence,directivity and stability of Hopf bifurcation have been analyzed in detail,and then,some judgments and criterions have been established to determine whether the ecological system has these specific dynamic behaviors.On this basis,the relevant dynamic simulation experiment have been carried out,the research findings show that time delay have a strong impact on dynamical behaviors of ecological system,especially show that two time delays how to synergy drive the ecological system to possess the Hopf bifurcation dynamical behavior.These results further reveal the influence mechanism of time delay on complex dynamical behavior of ecological systems.In chapter 3,it considered that the process of susceptible phytoplankton absorbing nutrient and converting their own energy can cause time delay and the process of susceptible phytoplankton translating into infectious phytoplankton can give rise to time delay,and then,a nutrient-phytoplankton ecological system with double time delays has been established.On this basis,the stability and Hopf bifurcation of the ecological system have been theoretically analyzed,and then,the critical conditions of these particular dynamical behaviors have been obtained.Finally,these results have some guiding significance for the prevention and control of large area outbreaks of phytoplankton.In chapter 4,it did some general summary to full text and showed the some shortcoming of the paper.