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论文:2017,Vol:35,Issue(2):316-320 |
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引用本文： |
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张莹, 都琳, 岳晓乐. Duffing映射的全局动力学行为分析与研究[J]. 西北工业大学学报 |
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Zhang Ying, Du Lin, Yue Xiaole. Analysis and Research on the Global Dynamical Behavior of Duffing Map[J]. Northwestern polytechnical university |
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| Duffing映射的全局动力学行为分析与研究 |
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| 张莹, 都琳, 岳晓乐 |
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| 西北工业大学 理学院, 陕西 西安 710072 |
| 摘要: |
| 针对二维离散Duffing映射，分别以a和b为分岔参数，借助多重分岔图、吸引子共存分析和吸引域分析等手段，对该映射系统的全局动力学行为进行了深入研究。研究结果表明，离散Duffing系统仅在一定参数范围内收敛；且随着参数的变化，虽然系统收敛区域的范围和收敛域中的动力学行为各不相同，但其变化均具有一定的规律性。最后，借助吸引子、吸引域及边界的分析，明确了共存吸引子间的关系及其变化规律，进一步探讨了系统不同动力学行为间的转迁机制。 |
| 关键词:
Duffing映射
对称破裂分岔
倍周期分岔
混沌
激变
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| Analysis and Research on the Global Dynamical Behavior of Duffing Map |
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| Zhang Ying, Du Lin, Yue Xiaole |
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| School of Nature and Applied Sciences, Northwestern Polytechnical University, Xi'an 710072, China |
| Abstract: |
| For the two-dimensional discrete Duffing map, the global dynamics is studied in depth by analyzing the multi-bifurcation diagrams, coexisting attractors, attraction basins, etc. The numerical results shows that Duffing map only converges in the certain regions of parameters, and the convergence regions are varying with the change of parameters. Although the dynamic behavior are complex, its evolution is of a certain regularity with the changing parameters. Finally, based on the analysis of attractors, attraction basins and basin boundaries, the relation and variation of coexisting attractors are explored, and the transformation mechanism between different dynamic behaviors in Duffing map is further investigated. |
| Key words:
Duffing map
symmetry breaking bifurcation
periodic doubling bifurcation
chaos
crisis
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| 收稿日期: 2016-09-27
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金（11672232、11302171）、陕西省自然科学基础研究计划（2016JQ1015）资助 |
| 通讯作者:
Email： |
| 作者简介: 张莹(1981-),女,西北工业大学副教授,主要从事非线性动力学的研究。
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| 作者相关文章 |
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| 张莹 在本刊中的所有文章 |
| 都琳 在本刊中的所有文章 |
| 岳晓乐 在本刊中的所有文章 |
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参考文献: |
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相关文献: |
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1．张莹, 李爽.重访Duffing系统中的对称破裂分岔与激变[J]. 西北工业大学学报, 2015,33(1): 88-92 |
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