Abstract
This paper mainly indicates the pest-control problem by using the biological control and the pesticide control. Firstly, it analyzed the continuous changing population of the three species-plants, plant pest and natural enemy-and the pesticides’ effects to establish a three-species model of the pests’ integrated control. Secondly, the pest equilibrium points with the natural enemy and that without natural enemy were obtained. We discussed the stability of the equilibrium points by the Hurwitz theorem and the first approximation method of stability and got the sufficient conditions for asymptotic stability. Finally, numerical simulations were performed by Matlab to analyze and verify the integrated control of plant pests in the situations with some natural enemies and without enemy. Moreover, the effects of spraying pesticides which have different killing rates on enemy and plant pest were analyzed.
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