Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Complex Dynamic Behaviors of an Impulsively Controlled Predator-prey System with Watt-type Functional Response

  • Baek, Hunki (Department of Mathematics Education, Catholic University of Daegu)
  • Received : 2015.04.16
  • Accepted : 2015.09.25
  • Published : 2016.09.23
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Abstract

In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.

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References

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