| 二维logistic映射的动力学行为和奇怪吸引子的分形特征 |
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| 引用本文： | 王立明. 二维logistic映射的动力学行为和奇怪吸引子的分形特征[J]. 大学物理, 2010, 29(2) |
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| 作者姓名： | 王立明 |
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| 作者单位： | 廊坊师范学院,物理系,河北,廓坊,065000 |
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| 基金项目： | 河北省廊坊市科学技术与发展指导计划资助项目(2009011002) |
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| 摘 要： | 研究了二维logistic映射的动力学行为和奇怪吸引子的分形特征.利用分岔图、相图和Lyapunov指数谱分析系统的分岔过程,研究系统通向混沌的道路并确定系统处于混沌运动的参数区间;采用G-P算法计算奇怪吸引子的关联维数和Kolmogorov熵,对奇怪吸引子的分形特征定量刻画;采用逃逸时间算法构造奇怪吸引子的彩色广义M-J集,对奇怪吸引子的分形特征定性表征.结果表明,这些分析方法的配合使用可以更全面、形象地描述奇怪吸引子的分形特征.
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| 关 键 词： | 二维logistic映射 Hopf分岔 关联维数 Kolmogorov熵:逃逸时间算法 广义M-J集 |
The dynamic behavior of two-dimensional logistic system and the fractal characterization of strange attractors |
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| WANG Li-ming. The dynamic behavior of two-dimensional logistic system and the fractal characterization of strange attractors[J]. College Physics, 2010, 29(2) |
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| Authors: | WANG Li-ming |
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| Affiliation: | Department of Physics;Langfang Teachers College;Langfang;Hebei 065000;China |
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| Abstract: | The dynamic behaviors of the two-dimensional logistic system are analyzed and the fractal characterization of strange attractors is researched.By using phase maps,bifurcation graphics and Lyapunov exponent,the paper reveals the transition of two-dimensional logistic system from regularity to chaos.By using G-P algorithm,the correlation dimension and Kolmogorov entropy of strange attractors are calculated,so the fractal characterization of strange attractors is described qualitatively.By using escape time al... |
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| Keywords: | two-dimensional logistic system Hopf bifurcation correlation dimension Kolmogorov entropy escape time algorithm general Mandelbrot-Julia sets |
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