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The Dynamics of a Prey–dependent Consumption Model Concerning Integrated Pest Management

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Abstract

A mathematical model for the dynamics of a prey–dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pest–eradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of prey–dependent consumption concerning integrated pest management are very complex, including period–doubling cascades, chaotic bands with periodic windows, crises, symmetry–breaking bifurcations and supertransients.

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Authors and Affiliations

  1. Department of Mathematics, Anshan Normal University, Anshan 114005, P. R. China

    Bing Liu

  2. College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P. R. China

    Bing Liu

  3. Deparment of Mathematics, Anshan Normal University, Anshan 114005, P. R. China

    Yu Juan Zhang

  4. Dalian University of Technology, Dalian 116024, P. R. China

    Yu Juan Zhang

  5. Institute of Mathematics, Academy of Mathematics and Systems Science, Beijing 100080, P. R. China

    Lan Sun Chen

  6. Dalian University of Technology, Dalian 116024, P. R. China

    Lan Sun Chen

  7. Dalian University of Technology, Dalian 116024, P. R. China

    Li Hua Sun

Authors
  1. Bing Liu
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  2. Yu Juan Zhang
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  3. Lan Sun Chen
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  4. Li Hua Sun
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Corresponding author

Correspondence to Bing Liu.

Additional information

This work is supported by National Natural Science Foundation of China (10171106), and supported by Science and Research Project Foundation of Liaoning Province Education Department

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Liu, B., Zhang, Y.J., Chen, L.S. et al. The Dynamics of a Prey–dependent Consumption Model Concerning Integrated Pest Management. Acta Math Sinica 21, 541–554 (2005). https://doi.org/10.1007/s10114-004-0476-2

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  • DOI: https://doi.org/10.1007/s10114-004-0476-2

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