| In this paper, we investigate the qualitative properties of solutions to a Holling typeⅡfunctional response three-species predator-prey system with im-pulse and diffusion.The full paper is divided into six chapters. The first chapter outlines the background and the research achievements. In the second chapter, the main def-initions and auxiliary results are provided. Sufficient condition was given for the existence of positively invariant set. ChapterⅢ, Sufficient conditions for the ex-istence of ultimate boundedness of solutions, permanence and the extinction of predator population in this system are established based on the upper and lower solution method and comparison theory of differential equation. ChapterⅣ, the compactness of the bounded solutions. ChapterⅤ, By constructing appropriate Lyapunov functions, we can obtain the conditions for the existence of a unique globally stable positive periodic solution. ChapterⅥ, Numerical illustrations. |
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