| 数值离散化对环面分支结构的影响 |
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| 引用本文： | 邹永魁,黄明游.数值离散化对环面分支结构的影响[J].东北数学,2002,18(2):151-166. |
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| 作者姓名： | 邹永魁 黄明游 |
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| 作者单位： | School of Mathematics，Jilin University，Changchun，130012 |
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| 基金项目： | The NSFC (10071030) of China，The Volkswagen Foundation of Germany，The Project-sponsored by SRP for ROCS, SEM (2002). |
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| 摘 要： | Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torus bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Predholm theory in Banach spaces is applied to obtain the global torus bifurcation. Our results complement those on the study of discretization effects of global bifurcation.
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| 关 键 词： | 微分方程 数值解法 参数化 动力系统 特征值 |
Torus Bifurcation Under Discretization |
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| ZOU Yongkui,and HUANG Mingyou.Torus Bifurcation Under Discretization[J].Northeastern Mathematical Journal,2002,18(2):151-166. |
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| Authors: | ZOU Yongkui and HUANG Mingyou |
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| Institution: | SchoolofMathematics,JilinUniversity,Changchun,130012 |
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| Abstract: | Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torns bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Fredholm theory in Banach spaces is applied to obtain the global torns bifurcation. Our results complement those on the study of discretization effects of global bifurcation. |
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| Keywords: | torus bifurcation symmetric scheme eigen-structure preserving scheme |
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