混沌系统不稳定周期轨道的搜索算法

岳毅宏; 韩文秀

引用本文:	岳毅宏，韩文秀.混沌系统不稳定周期轨道的搜索算法[J].控制理论与应用,2004,21(3):427~431.[点击复制]
	YUE Yi-hong, HAN Wen-xiu.Algorithms for searching unstable periodic orbits of chaotic systems[J].Control Theory and Technology,2004,21(3):427~431.[点击复制]

混沌系统不稳定周期轨道的搜索算法

Algorithms for searching unstable periodic orbits of chaotic systems

摘要点击 1941 全文点击 1883 投稿时间：2002-09-10 修订日期：2003-05-13

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DOI编号 10.7641/j.issn.1000-8152.2004.3.020

2004,21(3):427-431

中文关键词不稳定周期轨道(UPO's) UPO's搜索算法 Newton-Raphson算法(NR算法) Schmelcher-Diakonos(SD算法) NR-SD算法

英文关键词 unstable periodic orbits (UPO's) UPO's searching algorithm Newton-Raphson algorithm (NR algorithm) Schmelcher-Diakonos algorithm (SD algorithm) NR-SD algorithm

基金项目国家自然科学基金项目(79970043).

作者	单位
岳毅宏，韩文秀	天津大学管理学院，天津 300072

中文摘要

对混沌系统不稳定周期轨道(unstable periodic orbits,UPO's)的搜索算法进行了深入研究.首先分析了传统的Newton-Raphson算法(NR算法)及Schmelcher-Diakonos算法(SD算法)各自的优点和缺点.然后提出了一种新的UPO's搜索算法,称之为NR-SD算法.该方法集中了NR算法和SD算法各自的优点,能够在保证收敛全局性的条件下,极大地提高UPO's的搜索效率.此外,NR-SD算法采用了一种全新的初始点确定策略,该策略能够保证搜索到所有的长周期UPO's.最后借助于实例模拟验证了NR-SD算法的有效性,同时论证了周期p与p周期UPO's数目之间的关系.

英文摘要

The algorithms for searching unstable periodic orbits (UPO's) of chaotic systems are studied.Firstly,the advantages and disadvantages of the conventional Newton-Raphson algorithm (NR algorithm) and Schmelcher-Diakonos algorithm (SD algorithm) were respectively analyzed.Then,a new searching algorithm called NR-SD algorithm was proposed collecting advantages of both NR and SD algorithms:the global convergence guaranteed,the NR-SD algorithm greatly improves the searching efficiency.Moreover,in the NR-SD algorithm a new strategy of determining initial points was used so that all long-periodic UPO's could be found.Finally,the effectiveness of the NR-SD algorithm was verified by numerical simulation of an example.The relation between the period p and the number of p-periodic UPO's was established as well.