Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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DYNAMICS OF A ONE-PREY AND TWO-PREDATOR SYSTEM WITH TWO HOLLING TYPE FUNCTIONAL RESPONSES AND IMPULSIVE CONTROLS

  • Baek, Hunki (DEPARTMENT OF MATHEMATICS EDUCATION, CATHOLIC UNIVERSITY OF DAEGU)
  • Received : 2011.08.13
  • Accepted : 2012.09.15
  • Published : 2012.09.25
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Abstract

In this paper, we investigate the dynamic behaviors of a one-prey and two-predator system with Holling-type II functional response and defensive ability by introducing a proportion that is periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for predators at different fixed time. We establish conditions for the local stability and global asymptotic stability of prey-free periodic solutions by using Floquet theory for the impulsive equation, small amplitude perturbation skills. Also, we prove that the system is uniformly bounded and is permanent under some conditions via comparison techniques. By displaying bifurcation diagrams, we show that the system has complex dynamical aspects.

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