| 4维一般非线性动力系统规范形的计算 |
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| 引用本文： | 李静,杨朝欣,何斌.4维一般非线性动力系统规范形的计算[J].北京工业大学学报,2009,35(8):1138-1141. |
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| 作者姓名： | 李静 杨朝欣 何斌 |
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| 作者单位： | 北京工业大学应用数理学院,北京,100124;北京工业大学应用数理学院,北京,100124;北京工业大学应用数理学院,北京,100124 |
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| 基金项目： | 北京市自然科学基金资助项目(1082002);;国家自然科学基金资助项目(10732020) |
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| 摘 要： | 传统的规范形方法由于计算量大而且不利于计算机程序实现,很难应用于高维规范形的化简,为此,研究了4维一般非线性动力系统的规范形,以线性部分为1对双零根和1对纯虚根的Jordan标准形为例,采用改进共轭算子法,借助于Maple符号计算程序在不降维条件下,研究了动力系统的4维7阶规范形,并给出了通用的计算公式及系数对应关系.该方法易于计算机编程实现,能有效地处理高维规范形的化简.
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| 关 键 词： | 非线性动力系统 规范形 Maple符号程序 |
Normal Forms and Computation for Four-dimension of General Nonlinear Dynamical Systems |
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| LI Jing,YANG Chao-xin,HE Bin.Normal Forms and Computation for Four-dimension of General Nonlinear Dynamical Systems[J].Journal of Beijing Polytechnic University,2009,35(8):1138-1141. |
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| Authors: | LI Jing YANG Chao-xin HE Bin |
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| Affiliation: | College of Applied Sciences;Beijing University of Technology;Beijing 100124;China |
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| Abstract: | For the traditional method to computer normal form,it is hard to carry out for programming and reply to reduce normal forms for high dimension.The authors study the normal forms for general cases of the four-dimensional nonlinear dynamical systems.For Jordan forms of the linear parts with two double zero and a pair of pure imaginary eigenvalues,with the aid of Maple program and adjoint operator,the authors propose the computation formula and coefficients relations with original system for seven order normal... |
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| Keywords: | nonlinear dynamical system normal form Maple program |
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