| In this paper, the comparison theorem of impulsive differential equations and the Floquet theory are used to qualitatively analyze the integrated pest management models with periodic coefficients. Moreover, the applications of integrated pest management on agricultural production are studied deeply.In chapter 1, we introduce the background and research status on prey-predator system, which is based on integrated pest management tactics, and provides the readers with basic knowledge of the basic concepts and important lemmas that are frequently used in the following chapters.In chapter 2, we consider the dynamic behavior of a pest-predator model with impulsive control of different frequency of spraying pesticide and releasing the predators under the seasonal effect. The sufficient conditions of existence and global asymptotic stability of the pest-extinction periodic solution are obtained by Floquet theorem and little amplitude perturbation. Moreover, we analyze how the system parameters influence the critical value by numerical simulation.In chapter 3, the pest-predator model with different impulsive control and resistance development under the seasonal effect is proposed. The existence and global asymptotic stability of the pest-extinction periodic solution and the permanen-ce of the system are proved by the related theory of impulsive differential equations. Moreover, the numerical results show how the threshold is affected by system parameters. The study is hoped to provide theoretical basis for the practical production.Then we introduce the Monod-Haldane type response function, which will be more meaningful to actual production, into the system of the third chapter. As same as the proof methods that are used in the two front systems, we get the stability of the pest-eradication periodic solution and the permanence of the system through qualitative analysis.At last, it is a summary of this paper and a prospect of the researching on integrated pest management. |
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