切比雪夫序列初值精度有限时退化为周期序列

doi:10.13190/jbupt.201001.102.221

北京邮电大学学报 ›› 2010, Vol. 33 ›› Issue (1): 102-105.doi: 10.13190/jbupt.201001.102.221

切比雪夫序列初值精度有限时退化为周期序列

刘会师¹；余重秀¹；张琦^2，3；忻向军³

(1.北京邮电大学信息光子学与光通信研究院，北京 100876； 2.电子科技大学教育部宽带光纤传输与通信网技术重点实验室，成都 610054；3.北京邮电大学电子工程学院，北京 100876)

收稿日期:2009-04-24 修回日期:2009-06-29 出版日期:2010-02-28 发布日期:2010-02-28
通讯作者: 刘会师

Chebyshev Sequences Degenerating into Periodic Sequences with Realizing Finite Precision Initial Value

LIU Hui-shi¹；YU Chong-xiu¹；ZHANG Qi^2，3；XIN Xiang-jun³

(1.Institute of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China； 2.Key Laboratory of Broadband Optical Fiber Transmission and Communication Networks, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 610054, China； 3.School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China)

Received:2009-04-24 Revised:2009-06-29 Online:2010-02-28 Published:2010-02-28
Contact: LIU Hui-Shi

摘要/Abstract

摘要：

深入研究并分析切比雪夫序列的短周期现象，并通过数学证明，对于任意整数阶切比雪夫序列，在初值角度取有限小数时必会退化为短周期序列. 首先，通过证明得到切比雪夫序列退化为短周期序列的等价条件；然后，利用分类讨论的思想证明任意整数阶切比雪夫序列在初值角度取整数时，必会退化为短周期序列；最后，通过数学归纳法将这一结论扩展到任意有限精度初值上，得出切比雪夫序列在初值精度有限时退化为周期序列.

关键词: 混沌序列, 切比雪夫映射, 短周期

Abstract:

The short-period problems of Chebyshev sequences had been researched, and aconclusion that Chebyshev sequences of random integer order will degenerateinto short-period sequences while Chebyshev sequences initial value is afinite decimal had been proved. The equivalent conditions about Chebyshevsequences degenerating into short-period sequences had been shown first, andthen an integer order Chebyshev sequences whose initial value is integermust degenerate into short-period sequence has been proved. Finally, theinitial value conditions has been extended to finite decimal by usingmathematical induction method.

Key words: choatic sequences, chebyshev map, short periods

中图分类号:

O415.5

刘会师1 ；余重秀1 ；张琦2，3 ；忻向军3. 切比雪夫序列初值精度有限时退化为周期序列[J]. 北京邮电大学学报, 2010, 33(1): 102-105.

LIU Hui-shi¹；YU Chong-xiu¹；ZHANG Qi^2，3；XIN Xiang-jun³. Chebyshev Sequences Degenerating into Periodic Sequences with Realizing Finite Precision Initial Value[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2010, 33(1): 102-105.

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切比雪夫序列初值精度有限时退化为周期序列

Chebyshev Sequences Degenerating into Periodic Sequences with Realizing Finite Precision Initial Value

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