文章基本信息

标题：Global Hopf bifurcation for three-species ratio-dependent predator-prey system with two delays
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作者：Yunxian Dai ; Yusheng Jia ; Huitao Zhao 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：13
DOI：10.1186/s13662-015-0713-2
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, the effect of the two different delays on the dynamics of a three-species ratio-dependent predator-prey food-chain model is considered. By regarding the delay as the bifurcation parameter, the local stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Explicit formulas determining the properties of a Hopf bifurcation are obtained by using the normal form method and the center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delay τ 1 ≠ τ 2 $ au _) eq au_,$ . Finally, several numerical simulations supporting the theoretical analysis are also given.
关键词：predator-prey system ; ratio-dependent ; two delays ; Hopf bifurcation ; global Hopf bifurcation