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

Yunshyong  Chow; Sophia  Jang

doi:10.3934/dcdsb.2016019

Article Contents

2016, Volume 21, Issue 6: 1713-1728. Doi: 10.3934/dcdsb.2016019

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

Yunshyong Chow^1, and
Sophia Jang^2,

1.
Institute of Mathematics, Academia Sinica, Taipei 10617
2.
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042

Received: May 31, 2015

Revised: March 31, 2016

Published: July 2016

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Abstract

In this work, the effect of a host refuge on a host-parasitoid inter- action is investigated. The model is built upon a modied Nicholson-Bailey system by assuming that in each generation a constant proportion of the host is free from parasitism. We derive a sucient 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.

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Mathematics Subject Classification: Primary: 92D25; Secondary: 39A30.

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