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为了分析混沌序列的复杂度,文中采用强度统计复杂度算法分别对离散混沌系统(TD-ERCS)和连续混沌系统(简化Lorenz系统)进行复杂度分析,计算了混沌序列随参数变化的复杂度,分析了连续混沌系统产生的伪随机序列分别进行m序列和混沌伪随机序列扰动后的复杂度.研究表明,强度统计复杂度算法是一种有效的复杂度分析方法,离散混沌序列复杂度大于连续混沌序列复杂度,但对连续混沌系统的伪随机序列进行m序列和混沌伪随机序列扰动后可大大增加复杂度,为混沌序列在信息加密中的应用提供了理论依据.
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关键词:
- 强度统计复杂度算法 /
- TD-ERCS系统 /
- 简化Lorenz系统 /
- 序列扰动
To analyze the complexity of the chaotic sequences, based on the intensive statistical complexity algorithm, the complexities of the discrete TD-ERCS and continuous simplified Lorenz chaotic systems were investigated respectively, and the complexities of the chaotic sequences with different system parameters were calculated. The complexities of pseudo-random sequences of the continuous chaotic systems disordered by m-series and chaotic pseudo-random sequences were analyzed. The results indicate that the intensive statistical complexity algorithm is an effective method for analyzing the complexity of the chaotic sequences, and the complexity of the discrete chaotic systems is larger than that of the continuous ones. However, after disordering by m-series or chaotic pseudo-random sequences, the complexities of the pseudo-random sequences can be increased significantly. This study provides a theoretical basis for the applications of chaotic sequences in the field of secure communication and information encryption.-
Keywords:
- intensive statistical complexity algorithm /
- TD-ERCS /
- simplified Lorenz system /
- sequence disorder
[1] Li M, Vitanyi P M B 1990 Amsterdam: Elsevier Science A 187
[2] Lempel A, Ziv J 1976 IEEE Trans IT-22 75
[3] Steven M, Pincus S 1991 Mathematics 88 2297
[4] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[5] Sun K H, Tan G Q, Sheng L Y 2008 Acta Phys. Sin. 57 3359 (in Chinese) [孙克辉、谈国强、盛利元 2008 物理学报 57 3359]
[6] López-Ruiz R, Mancini H L, Calbet X 1995 Phys. Lett. A 209 321
[7] Larrondo H A, González C M, Martin M T, Plastino A, Rosso O A 2005 Physica A 356 133
[8] González C M, Larrondo H A, Rosso O A 2005 Physica A 354 281
[9] Sheng L Y, Sun K H, Li C B 2004 Acta Phys. Sin. 53 2871 (in Chinese) [盛利元、孙克辉、李传兵 2004 物理学报 53 2871]
[10] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese) [肖方红、阎桂荣、韩宇航 2004 物理学报 53 2877]
[11] Lü J H, Chen G R, Zhang S C, elikovsk Dy＇ S 2002 Int.J.Bifurc.Chaos 12 2917
[12] Sun K H, Sprott J C 2009 J. Bifurcation and Chaos 19 1357
[13] Wang L, Wang F P, Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 物理学报 55 3964]
[14] Luo S J, Qiu S S, Chen X 2010 Journal of South China University of Technology 38 18 (in Chinese) [罗松江、丘水 生、陈 旭 2010 华南理工大学报 38 18] 〖15] Fan X Q 2009 Computer Engineering & Science 31 20 (in Chinese) [范雪琴 2009 计算机工程与科学 31 20]
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[1] Li M, Vitanyi P M B 1990 Amsterdam: Elsevier Science A 187
[2] Lempel A, Ziv J 1976 IEEE Trans IT-22 75
[3] Steven M, Pincus S 1991 Mathematics 88 2297
[4] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[5] Sun K H, Tan G Q, Sheng L Y 2008 Acta Phys. Sin. 57 3359 (in Chinese) [孙克辉、谈国强、盛利元 2008 物理学报 57 3359]
[6] López-Ruiz R, Mancini H L, Calbet X 1995 Phys. Lett. A 209 321
[7] Larrondo H A, González C M, Martin M T, Plastino A, Rosso O A 2005 Physica A 356 133
[8] González C M, Larrondo H A, Rosso O A 2005 Physica A 354 281
[9] Sheng L Y, Sun K H, Li C B 2004 Acta Phys. Sin. 53 2871 (in Chinese) [盛利元、孙克辉、李传兵 2004 物理学报 53 2871]
[10] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese) [肖方红、阎桂荣、韩宇航 2004 物理学报 53 2877]
[11] Lü J H, Chen G R, Zhang S C, elikovsk Dy＇ S 2002 Int.J.Bifurc.Chaos 12 2917
[12] Sun K H, Sprott J C 2009 J. Bifurcation and Chaos 19 1357
[13] Wang L, Wang F P, Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 物理学报 55 3964]
[14] Luo S J, Qiu S S, Chen X 2010 Journal of South China University of Technology 38 18 (in Chinese) [罗松江、丘水 生、陈 旭 2010 华南理工大学报 38 18] 〖15] Fan X Q 2009 Computer Engineering & Science 31 20 (in Chinese) [范雪琴 2009 计算机工程与科学 31 20]
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