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Complexity Of A Delayed Predator–Prey Model With Impulsive Harvest And Holling Type Ii Functional Response

Author

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  • GUANGZHAO ZENG

    (Department of Mathematics, Shaoguan University, Shaoguan, Guangdong, 512005, P. R. China)

  • FENGYAN WANG

    (College of Science, Jimei University, Xiamen, Fujian, 361021, P. R. China)

  • JUAN J. NIETO

    (Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Spain)

Abstract

We study an impulsive delay differential predator–prey model with Holling type II functional response. The stability of the trivial equilibrium is analyzed by means of impulsive Floquet theory providing a sufficient condition for extinction. Using coincidence degree theory we show the existence of positive periodic solutions. The system is then analyzed numerically, revealing that the presence of delays and impulses may lead to chaotic solutions, quasi-periodic solutions, or multiple periodic solutions. Several simulations and examples are presented.

Suggested Citation

  • Guangzhao Zeng & Fengyan Wang & Juan J. Nieto, 2008. "Complexity Of A Delayed Predator–Prey Model With Impulsive Harvest And Holling Type Ii Functional Response," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 77-97.
    • Handle: RePEc:wsi:acsxxx:v:11:y:2008:i:01:n:s0219525908001519
    DOI: 10.1142/S0219525908001519
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    Cited by:

    1. Boonrangsiman, S. & Bunwong, K. & Moore, Elvin J., 2016. "A bifurcation path to chaos in a time-delay fisheries predator–prey model with prey consumption by immature and mature predators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 16-29.

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