NEIMARK-SACKER BIFURCATIONS IN A HOST-PARASITOID SYSTEM WITH A HOST REFUGE

被引：13

作者：

Chow, Yunshyong ^{[1
]}

Jang, Sophia ^{[2
]}

机构：

[1] Acad Sinica, Inst Math, Taipei 10617, Taiwan

[2] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 06期

关键词：

Host-parasitoid; spatial refuge; Neimark-Sacker bifurcation; uniform persistence; PREDATOR-PREY MODEL; COMMUNITY STRUCTURE; PERSISTENCE; DISTURBANCE;

D O I：

10.3934/dcdsb.2016019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1713 / 1728

页数：16

共 23 条

[1]

Allen L. J., 2006, An introduction to mathematical biology

[2]

Begon M., 1996, ECOLOGY

[3] ROLE OF PREY DISPERSAL AND REFUGES ON PREDATOR-PREY DYNAMICS [J].