Bifurcations And Stability Of A Discrete Singular Bioeconomic System

The thesis analyzes the stability and bifurcations of a discrete singular bioeconomicsystem in the closed first quadrant R_+~3. First, applying the Poincare scheme to a differential-algebraic predator-prey system where the economic interest of harvesting is taken into ac-count, a discrete singular bioeconomic system is proposed. Then, local stability and theexisting conditions and directions of bifurcations around the interior fixed points of the pro-posed model are discussed by using the normal form, the center manifold theorem and thebifurcation theory of the discrete singular bioeconomic system under the influence of thestep δ and the fishing economic interests m respectively.This thesis is divided into four chapters:The first chapter introduces the research background, the modeling process, and thebasic results and innovation points.The second chapter mainly studies the local stability and the existing conditions of thebifurcations of the discrete singular bioeconomic system (1.4) under the influence of the stepδ and the fishing economic interests m respectively.The third chapter mainly researches the bifurcation directions of of the discrete singularbioeconomic system (1.4) by selecting the step δ and the fishing economic interests m asbifurcation parameters respectively. And by MATLAB numerical simulation, we not onlyverify the correctness and rationality of our theoretical results, but also show the complexdynamic behaviors of the system.The last chapter of this paper provides a summary and an outlook.