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Mathematical Biosciences and Engineering

2005, Volume 2, Issue 2: 329-344. doi: 10.3934/mbe.2005.2.329
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Impulsive Ecological Control Of A Stage-Structured Pest Management System

  • 1.
    Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004
  • 2.
    School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083
  • Received: 01 July 2004 Accepted: 29 June 2018 Published: 01 March 2005

  • MSC : 34A37, 92D25.

  • The dynamics of a stage-structured pest management system is studied by means of autonomous piecewise linear systems with impulses governed by state feedback control. The sufficient conditions of existence and stability of periodic solutions are obtained by means of the sequence convergence rule and the analogue of the Poincaré criterion. The attractive region of periodic solutions is investigated theoretically by qualitative analysis. The bifurcation diagrams of periodic solutions are obtained by using the Poincaré map, as well as the chaotic solution generated via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed.

    Citation: Guirong Jiang, Qishao Lu, Linping Peng. Impulsive Ecological Control Of A Stage-Structured Pest Management System[J]. Mathematical Biosciences and Engineering, 2005, 2(2): 329-344. doi: 10.3934/mbe.2005.2.329

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  • The dynamics of a stage-structured pest management system is studied by means of autonomous piecewise linear systems with impulses governed by state feedback control. The sufficient conditions of existence and stability of periodic solutions are obtained by means of the sequence convergence rule and the analogue of the Poincaré criterion. The attractive region of periodic solutions is investigated theoretically by qualitative analysis. The bifurcation diagrams of periodic solutions are obtained by using the Poincaré map, as well as the chaotic solution generated via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed.


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  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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