| 时滞系统稳定性与Hopf分岔的迭代法 |
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| 引用本文： | 王在华.时滞系统稳定性与Hopf分岔的迭代法[J].科技导报(北京),2009,27(2). |
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| 作者姓名： | 王在华 |
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| 作者单位： | 南京航空航天大学航空宇航学院,南京,210016;中国人民解放军理工大学理学院,南京,211101
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| 基金项目： | 国家自然科学基金，教育部全国优秀博士学位论文作者专项基金 |
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| 摘 要： | 简要综述了迭代法在时滞系统稳定性与Hopf分岔研究中的若干新进展.在稳定性分析中,利用Lambert W函数,时滞系统的最大实部特征根可以用Newton-Raphson等迭代法求得.而在Hopf分岔分析中.利用迭代法求得了分岔周期解的近似表达式.对这两个问题,迭代法简便有效.
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| 关 键 词： | 时滞系统 稳定性 Hopf分岔 迭代法 |
Applications of Iterative Methods to Studies on Stability and Hopf Bifurcation of Time-Delay Systems |
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| WANG Zaihua Institute of Science,PLA University of Science , Technology,Nanjing ,China College of Aerospace Engineering,Nanjing University of Aeronautics , Astronautics,Nanjing ,China.Applications of Iterative Methods to Studies on Stability and Hopf Bifurcation of Time-Delay Systems[J].Science & Technology Review,2009,27(2). |
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| Authors: | WANG Zaihua Institute of Science PLA University of Science Technology Nanjing China College of Aerospace Engineering Nanjing University of Aeronautics Astronautics Nanjing China |
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| Institution: | WANG Zaihua Institute of Science,PLA University of Science , Technology,Nanjing 211101,China College of Aerospace Engineering,Nanjing University of Aeronautics , Astronautics,Nanjing 210016,China |
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| Abstract: | This paper presents a brief review on the recent advances in applications of iterative methods to studies on stability and Hopf bifurcation of time-delay systems. In stability analysis, the Newton-Raphson iterative method is used to calculate the rightmost characteristic root(s), with the help of the Lambert W function. In Hopf bifurcation analysis, the iterative method is applied for finding an approximate solution of the bifurcated periodic solution. In both cases, the iterative methods are very effective... |
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| Keywords: | time-delay systems stability Hopf bifurcation iterative method |
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