| 一类复杂流行病学模型的混沌研究 |
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| 引用本文： | 狄根虎,许勇,徐伟,顾仁财.一类复杂流行病学模型的混沌研究[J].物理学报,2011,60(2):20504-020504. |
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| 作者姓名： | 狄根虎 许勇 徐伟 顾仁财 |
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| 作者单位： | 西北工业大学应用数学系,西安 710129 |
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| 基金项目： | 国家自然科学基金(批准号:10972181,11002001,10872165,10932009)、西北工业大学基础研究基金和翱翔之星资助的课题. |
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| 摘 要： | 研究了一类周期变化的非线性复杂发病率的广义流行病学模型(SIR(susceptible, infected, recovered)模型). 通过一系列坐标变换将原模型转化为Hamilton系统,运用Melnikov方法证明了该系统存在混沌运动,给出了发生同宿分岔的条件,并用数值模拟验证了上述结果.
关键词：
SIR(susceptible
infected
recovered)模型
混沌运动
Melnikov方法
同宿分岔
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| 关 键 词： | SIR(susceptible infected recovered)模型 混沌运动 Melnikov方法 同宿分岔 |
| 收稿时间： | 2010-05-15 |
Chaos for a class of complex epidemiological models |
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| Di Gen-Hu,Xu Yong,Xu Wei,Gu Ren-Cai.Chaos for a class of complex epidemiological models[J].Acta Physica Sinica,2011,60(2):20504-020504. |
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| Authors: | Di Gen-Hu Xu Yong Xu Wei Gu Ren-Cai |
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| Institution: | Di Gen-Hu Xu Yong Xu Wei Gu Ren-Cai (Department of Applied Mathematics,Northwestern Polytechnical University,Xi'an 710129,China ) |
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| Abstract: | We study the well-known SIR (susceptible, infected, recoverd) model with nonlinear complex incidence rates. Firstly,a series of coordinate transformations are carried out to change the equations as the amenable Hamiltonian systems. Secondly the Melnikov's method is used to establish the conditions of existence of chaotic motion and find the analytically critical values of homoclinic bifurcation. Good agreement can be found between numerical results and analytical results. |
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| Keywords: | SIR(susceptible infected recoverd) model chaotic motion Melnikov's method homoclinic bifurcation |
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