Neimark-sacker bifurcations in a host-parasitoid system with a host refuge

Yunshyong Chow, Sophia Jang

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9 Scopus citations


In this work, the effect of a host refuge on a host-parasitoid interaction is investigated. The model is built upon a modified Nicholson-Bailey system by assuming that in each generation a constant proportion of the host is free from parasitism. We derive a sufficient condition based on the model parameters for both populations to coexist. We prove that it is possible for the system to undergo a supercritical and then a subcritical Neimark-Sacker bifurcation or for the system only to exhibit a supercritical Neimark-Sacker bifurcation. It is illustrated numerically that a constant proportion of host refuge can stabilize the host-parasitoid interaction.

Original languageEnglish
Pages (from-to)1713-1728
Number of pages16
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number6
StatePublished - Aug 2016


  • Host-parasitoid
  • Neimark-Sacker bifurcation
  • Spatial refuge
  • Uniform persistence


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