| 一个新四维混沌系统的Hopf分岔分析 |
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| 引用本文： | 杜文举,俞建宁,张建刚,张莉,安新磊.一个新四维混沌系统的Hopf分岔分析[J].温州大学学报(自然科学版),2014(1):31-38. |
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| 作者姓名： | 杜文举 俞建宁 张建刚 张莉 安新磊 |
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| 作者单位： | [1]兰州交通大学数理学院,甘肃兰州730070 [2]兰州工业学院基础学科部,甘肃兰州730050 |
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| 基金项目： | 国家自然科学基金项目（11161027,61364001）;教育部科技研究重点项目（212180） |
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| 摘 要： | 通过非线性动力学理论，分析了一个四维混沌系统平衡点的稳定性及其基本动力学特性，并通过中心流形理论和范式理论，给出了决定系统周期解稳定性和方向的表达式．最后，通过数值仿真证明了理论分析的正确性．
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| 关 键 词： | 四维混沌系统 Hopf分岔 Poincae截面 Lyapunov指数 范式理论 |
The Hopf Bifurcation Analysis of a Novel Four-dimensional Chaotic System |
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| DU Wenju,YU Jianning,ZHANG Jiangang,ZHANG Li,AN Xinlei.The Hopf Bifurcation Analysis of a Novel Four-dimensional Chaotic System[J].Journal of Wenzhou University Natural Science,2014(1):31-38. |
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| Authors: | DU Wenju YU Jianning ZHANG Jiangang ZHANG Li AN Xinlei |
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| Institution: | 1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, China 730070; 2. Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou, China 730050) |
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| Abstract: | The stability of the equilibrium points and basic dynamic properties of the nonlinear system are analyzed via nonlinear dynamics theory, and the formulae for determining the stability and direction of bifurcating periodic solutions are derived via central manifold theorem and normal form theory. Finally, a numerical example is provided for justifying the validity of the theoretical analysis |
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| Keywords: | Four-dimensional Chaotic System Hopf Bifurcation Poincar6 Sections Lyapunov Exponents Normal Form Theory |
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