文章基本信息

标题：Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay
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作者：Yakui Xue ; Xiaoqing Wang
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2012
卷号：2012
DOI：10.1155/2012/252437
出版社：Hindawi Publishing Corporation
摘要：A predator-prey system with disease in the predator is investigated, where the discrete delay 𝜏 is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when 𝜏 crosses some critical values. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived.