| HOPF BIFURCATION AND OTHER DYNAMICAL BEHAVIORS FOR A FOURTH ORDER DIFFERENTIAL EQUATION IN MODELS OF INFECTIOUS DISEASE |
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| 引用本文： | 井竹君,刘正荣,沈家琦.HOPF BIFURCATION AND OTHER DYNAMICAL BEHAVIORS FOR A FOURTH ORDER DIFFERENTIAL EQUATION IN MODELS OF INFECTIOUS DISEASE[J].应用数学学报(英文版),1994,10(4):401-410. |
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| 作者姓名： | 井竹君 刘正荣 沈家琦 |
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| 作者单位： | JING ZHUJUN(Institute of Mathematics，the Chinese Academy of Sciences，Beijing 100080，China and Institute of Mechanics，the Chinese Academy of Sctences (uisitor)，Beijing 100080，China)LIU ZHENGRONG(Department of Mathematics，Yunnan University，Kunming 6500 |
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| 摘 要： | ＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＡＮＤＯＴＨＥＲＤＹＮＡＭＩＣＡＬＢＥＨＡＶＩＯＲＳＦＯＲＡＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＩＮＭＯＤＥＬＳＯＦＩＮＦＥＣＴＩＯＵＳＤＩＳＥＡＳＥＪＩＮＧＺＨＵＪＵＮ（井竹君）（Ｉｎｓｔｉｔ...
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| 收稿时间： | 18 May 1991 |
Hopf bifurcation and other dynamical behaviors for a fourth order differential equation in models of infectious disease |
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| Zhujun Jing,Zhengrong Liu,Jiaqi Shen.Hopf bifurcation and other dynamical behaviors for a fourth order differential equation in models of infectious disease[J].Acta Mathematicae Applicatae Sinica,1994,10(4):401-410. |
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| Authors: | Zhujun Jing Zhengrong Liu Jiaqi Shen |
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| Institution: | (1) Institute of Mathematics, the Chinese Academy of Sciences, 100080 Beijing, China;(2) Institute of Mechanics, the Chinese Academy of Sciences (visitor), 100080 Beijing, China;(3) Department of Mathematics, Yunnan University, 650091 Kunming, China;(4) Yunnan Institute of Applied Mathematics, 650091 Kunming, China;(5) Department of Mathematics, Shanghai Normal University, 200234 Shanghai, China |
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| Abstract: | Periodic solutions of Hopf type and other dynamical behaviors for a four-order differential equation which occurs in the model of infections disease are investigated. The extended theorem about the conditions for the existence of Hopf bifurcation is proved in higher-order differential equations with several parameters. The Hopf bifurcation value is given through the medium of the corresponding coordinate at the Hopf bifurcation point, and depends on one parameter.The paper reveals that the model of Holt and Picker has periodic solutions, and proves the reliability of the numerical solution which is given by Liu Winmin. |
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| Keywords: | Model of infections disease existence and stability of equilibria Hopf bifurcation |
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