| With studying the predator-prey system with harvesting rate by qualitative analysis, it predicts the development and change of population and to analyze the capture behaviors effect on the population. We can decide how much capture quantity is to maintain the balance of ecological system and to satisfy the need, when capture quantity reaches the top. From these facts, it is very important that the system with harvesting rate relates to the problem of resource continuable development, because it guides to renew the resources to carry on reasonable of exploitation and utility.At present, to the research of predator-prey system with constant harvesting rate simultaneity study little, on the basis of work which has been done, therefore this paper makes further study on the equilibrium point of predator-prey system with constant harvesting rate. Firstly, it discusses a class of predator-prey system with Hollingâ…¡,â…¢functional response in linear dense restrict prey system. With using general qualitative analysis methods, and in virtue of the function property of the isoclinic line, it protracts the image of the isoclinic line, and gets the conditions of existence of equilibrium point and the boundary property of the solution, and the conditions of inexistence of the close curve and the qualitative of the equilibrium point in the conditions of prey-predator system with constant harvesting rate. To the general functional response model with constant harvesting rate simultaneity, it gets the stability of the equilibrium point and the boundary property of the solution and the conditions of inexistence of close curve with utilizing qualitative analysis methods.Concerning Kolmogorov model of constant harvesting rate simultaneity, this paper still sets out a class of Kolmogorov model, in virtue of qualitative analysis methods and the relation of the root and coefficient of the corresponding equation of the isoclinic line, portracts the trend of the isoclinic line, judge the...
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