Qualitative Analysis Of A Class Of The Monod-of Haldane Functional Response And Stage Structure Of Predator System

The goal of this paper is to study systematically a predator-prey mode consisting of one prey and one predator species which include immature stage and mature stage. The Mon od-Haldane functional response is used in the predator-prey system. By applying qualitative analysis, then we take the sufficient condition for the overall stability to the model of the boundary equilibrium point R1, (1,0,0), and by choosing some appropriate parameters to obtain the criterion of the positive equilibrium R3 (χ0,yo,z0) which is partially stable. At the end of my paper, I will use the MATLAB software to provide two examples which can demonstrate these conclusions in my thesis.This paper is divided into three chapters. The first chapter introduces the research background of mathematical biology. Then introduces some common functional responses and a research survey of models with stage structure. Finally, it puts forward the work needed to be studied in this thesis. Chapter two is the main content of this paper, it studies the criterion of the existence and stability of the prey equilibrium point, and my main task is to deduce the sufficient condition of the positive equilibrium R3(χ0,y0,z0), and it provides instances to verify these conclusions. Chapter three is a summary of the thesis, and it also rises what needs to be improved in this paper.