具有B-DA功能项的时滞传染病模型的稳定性与Hopf分岔的分析
Stability and Hopf Bifurcation for an Epidemic Model with B-DA and Delay
DOI: 10.12677/MOS.2016.54023, PDF,    国家自然科学基金支持
作者: 邱成燕, 黄东卫*, 郭永峰：天津工业大学理学院，天津；刘雍：天津工业大学纺织学院，教育部纺织复合材料重点实验室，天津
关键词: 时滞模型；稳定性；Hopf分岔；Hopf-Zero分岔；Delay Model； Stability； Hopf Bifurcation； Hopf-Zero Bifurcation
摘要: 本文建立了带有Beddington-DeAngelis功能项的时滞传染病模型。对于模型的研究，我首先从模型特征方程的特征根进行研究，其次再分析了模型正平衡点的稳定性，接着确定了该模型的稳定性区域，从而发现当模型中的时滞满足一系列的条件时，模型经历Hopf分岔和Hopf-Zero分岔，最后通过数值模拟验证了理论的正确性。
Abstract: In this paper, we built an epidemic model with Beddington-DeAngelis and delay. First, we analyzed the associated characteristic equation, and then discussed the stability of the equilibrium. Finally, we determined the stability region of the model. Moreover, we found that when the time delay in the model satisfies a series of conditions, the model undergoes Hopf bifurcations and Hopf-Zero bifurcation. Finally, some numerical simulations and phase diagram are given to satisfied theoretical results.
文章引用：邱成燕, 黄东卫, 郭永峰, 刘雍. 具有B-DA功能项的时滞传染病模型的稳定性与Hopf分岔的分析[J]. 建模与仿真, 2016, 5(4): 183-190. http://dx.doi.org/10.12677/MOS.2016.54023

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