Kyungpook Mathematical Journal

  • 제50권2호
  • /
  • Pages.255-266
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  • 2010
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Global Periodic Solutions in a Delayed Predator-Prey System with Holling II Functional Response

  • 투고 : 2009.06.16
  • 심사 : 2010.01.27
  • 발행 : 2010.06.30
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초록

We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are given.

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참고문헌

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피인용 문헌

  1. Global Hopf Bifurcation for a Predator–Prey System with Three Delays vol.27, pp.07, 2017, https://doi.org/10.1142/S0218127417501085