The Stability And Bifurcation Analysis Of Discrete-time Prey-predator Systems With A Variable Harvesting Item

The paper mainly studies the stability and bifurcation of two discrete-time prey-predatorsystems with a variable harvesting item and consists of four chapters.The first chapter as an introduction,introduces the research background,the actual sig-nificance and the present research situation of the system.And the related knowledge whichis needed in the paper is addressed.The first chapter for the introduction, introduced the research background of such asystem, the actual significance, the present research situation and the related knowledge of.In the second chapter,the dynamics behaviors of a discrete-time prey-predator systemof Leslie-Holling type with a variable harvesting item are discussed.First of all,we investi-gate the existence and stability of the positive fixed points.Then we discuss that the systemundergoes flip bifurcation and Hopf bifurcation when the bifurcation parameter passes somecritical values by using the center manifold theorem and bifurcation theory.And the relevantresults are given.Finally, computer simulations are presented to illustrate the results.In the third chapter,we discuss a discrete-time prey-predator system of Smith-Hollingtype with a variable harvesting item,including the existence and stability of the positive fixedpoints, and the conditions which the system need to satisfy to undergo flip bifurcation andHopf bifurcation at the positive fixed points.Also we give the corresponding results.Finally,computer simulations are also presented to illustrate the results.The chaper four summarizes the mainly work of this paper and points out some of thesubject as a further study.