| 一类具有时滞的干扰模型的Hopf分支 |
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| 引用本文： | 阙军霞,李必文,李中文.一类具有时滞的干扰模型的Hopf分支[J].湖北师范学院学报(自然科学版),2011,31(3):65-70. |
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| 作者姓名： | 阙军霞 李必文 李中文 |
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| 作者单位： | 湖北师范学院数学与统计学院,湖北黄石,435002 |
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| 摘 要： | 讨论了一类具有时滞的干扰的单种群模型的无条件稳定性以及Hopf分支的存在唯一性。首先,利用特征值理论得到了模型无条件稳定性的充要条件,从而说明时滞为无害时滞;再以时滞τ为参数,给出了Hopf分支的存在唯一性及分支值处模型平衡态的稳定性的条件;最后举例验证了定理的可实现性,利用Matlab得到其参数取不同值时的曲线拟合图。
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| 关 键 词： | 时滞干扰模型 Hopf分支 无条件稳定性 |
The Hopf bifurcation of a class of interference model with time delay |
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| QUE Jun-xia,LI Bi-wen,LI Zhong-wen.The Hopf bifurcation of a class of interference model with time delay[J].Journal of Hubei Normal University(Natural Science),2011,31(3):65-70. |
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| Authors: | QUE Jun-xia LI Bi-wen LI Zhong-wen |
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| Institution: | QUE Jun-xia,LI Bi-wen,LI Zhong-wen (College of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China) |
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| Abstract: | The unconditional stability and existence of a unique Hopf bifurcation are discussed for a class of interence model with delay.First of all,the sufficient and necessary condition of unconditional stability is obtained according to the eigenvalue theory.Consequently it is implied that the time delay is harmless one.Then the condition of existence of a unique Hopf bifurcation and stability of equilibrium state in bifurcation values is derived when time delay is a parameter.In the end,the achievability of the ... |
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| Keywords: | interference model with time delay Hopf bifurcation unconditional stability |
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