Impulsive Ecological Control Of A Stage-Structured Pest Management System
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Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004
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School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083
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Received:
01 July 2004
Accepted:
29 June 2018
Published:
01 March 2005
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MSC :
34A37, 92D25.
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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.
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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Abstract
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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