| 非线性动力系统周期解的初值同伦方法 |
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| 引用本文： | 张丽清,徐宝民.非线性动力系统周期解的初值同伦方法[J].中山大学学报论丛,1996(5). |
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| 作者姓名： | 张丽清 徐宝民 |
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| 作者单位： | 华南理工大学电子与信息学院 |
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| 摘 要： | 本文研究动力系统周期解的同伦方法．首先将周期解的定解问题转化为非线性代数方程组，给出其单调同伦求解方法．并利用数值积分方法确定代数方程组的值及其Ｊａｃｏｂｉ矩阵，从而证明了数值解的存在性并出其误差估计．最后的数值实例说明了该方法的有效性
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| 关 键 词： | 混沌，周期解，同伦方法，Jacobi矩阵 |
The Initial Value Homotopy Method for Periodic Solutions of Nonlinear Dynamical Systems |
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| Zhang Liqing\ Xu Baomin.The Initial Value Homotopy Method for Periodic Solutions of Nonlinear Dynamical Systems[J].Supplement to the Journal of Sun Yatsen University,1996(5). |
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| Authors: | Zhang Liqing\ Xu Baomin |
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| Abstract: | This paper deals with the homotopy methods for solving periodic solutions of dynamical systems. The problem for periodic solutions is formulated into the nonlinear algebraic system. Then a monotone homotopy method is proposed to solve the nonlinear system. To evaluate the value and its Jacobian matrix a numerical integration method is employed. The error estimate of the numerical solution is also given. Fianlly a numerical example is given to illustrate the effectiveness of the method. |
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| Keywords: | periodic solutions homotopy methods nonlinear systems |
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