Study On The Dynamic Problems Of Several Classes Of Ecological Systems With Time Delay

In this paper, we discuss several classes of ecological systems with time delay, and theoretically explore the ecological system dynamics related issues, as well as deeply explain the complex dynamic phenomena of the ecological system, and obtain some good results.Firstly, we construct a nutrient-phytoplankton ecological system with double time delays, prove the existence of the positive equilibrium point, derive the threshold conditions which can lead to local steady state transformation and Hopf bifurcation, study the Hopf branch direction and stability of periodic solutions of a branch, reveal influence mechanism of the time delay on the dynamic evolution of the ecological system. In addition, the relevant dynamic simulation experiments were carried out to verify the feasibility and the validity of the theoretical analysis results,and further to explain the time delay how to affect dynamic evolution process ecological system.Secondly, we study the dynamics properties of a phytoplankton-zooplankton ecological system with time delay and Crowley-Martin functional response. In the case of time delay exists and noexists,respectively, analyse the dissipation and persistence of the ecological system, as well as investigate the local and global asymptotic stability of the equilibrium point, further explore the existence of Hopf branch, Hopf branch directional branch and its stability of periodic solutions.Meanwhile, the local stability result shows that the disturbance of plankton population will not appear under the condition of certain parameters. Furthermore, under the global stability criteria, the relevant dynamic simulation experiments were carried out to show that the time delay will not change the internal stability of ecological system.Finally, we establish a change Leslie-Gower prey-predator ecological system with double time delays, discuss the dissipation and persistence of the ecological system, give the global stability criterion of the positive equilibrium, analyze the local stability of the positive equilibrium and the existence of Hopf bifurcation, as well as determine the Hopf branch direction and the stability of bifurcated periodic solutions. At the same time, we carry out relevant dynamic simulation experiments of the ecological system to reveal that the time delay can seriously affect dynamic behaviors of the ecological system, especially the time delay can lead to the ecological system to undergo dynamic behavior evolution process in the form of equilibrium state? periodic motion? quasi-periodic motion? chaotic motion.