American Institute of Mathematical Sciences

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August  2004, 4(3): 759-768. doi: 10.3934/dcdsb.2004.4.759

Modelling and analysis of integrated pest management strategy

Sanyi Tang 1, and  Lansun Chen 1,

1. 

Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China, China

Received  November 2002 Revised  February 2004 Published  May 2004

Two impulsive models concerning integrated pest management(IPM) are proposed according to impulsive effect with fixed moments and unfixed moments, respectively. The first model has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaching the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. By using analytical method, we show that there exists an orbitally asymptotically stable periodic solution with a maximum value no larger than the given economic threshold. Further, the complete expression of period of the periodic solution is given. Thus, IPM strategy proved firstly by mathematical models is more effective than the classical method.
Keywords: state-dependent impulsive differential equations, periodic solution., IPM strategy, economic threshold.
Mathematics Subject Classification: 34A37, 47N6.
Citation: Sanyi Tang, Lansun Chen. Modelling and analysis of integrated pest management strategy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 759-768. doi: 10.3934/dcdsb.2004.4.759
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