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The Dynamics of a Predator-prey Model with Ivlev’s Functional Response Concerning Integrated Pest Management

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Abstract

A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one.

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Authors and Affiliations

  1. Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114005, China

    Bing Liu & Ying Zhi

  2. Academy of Mathematics and Systems Science, Beijing 100080, China

    Bing Liu & Lan-sun Chen

  3. Dalian University of Technology, Dalian 116024, China

    Lan-sun Chen

Authors
  1. Bing Liu
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  2. Ying Zhi
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  3. Lan-sun Chen
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Correspondence to Bing Liu.

Additional information

Supported by National Natural Science Foundation of China (No. 10171106).

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Liu, B., Zhi, Y. & Chen, Ls. The Dynamics of a Predator-prey Model with Ivlev’s Functional Response Concerning Integrated Pest Management. Acta Mathematicae Applicatae Sinica, English Series 20, 133–146 (2004). https://doi.org/10.1007/s10255-004-0156-0

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  • DOI: https://doi.org/10.1007/s10255-004-0156-0

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