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为了准确分析混沌序列的复杂性, 采用模糊熵算法(FuzzyEn) 对典型离散混沌系统和连续混沌系统的复杂度进行分析. 与近似熵(ApEn)、 样本熵(SampEn) 和强度统计复杂度算法相比, FuzzyEn算法是一种更有效的混沌复杂度测度算法, 且对相空间维数(m)、 相似容限度(r) 和序列长度(N) 的敏感性、 依赖性更低, 鲁棒性和测度值的连续性更好. 对混沌系统的复杂性分析表明, 连续混沌系统的复杂度远小于离散混沌系统, 但是如果利用高复杂度的离散混沌伪随机序列或经典 m序列对连续混沌系统产生的伪随机序列进行扰动, 则能大大提高混沌序列的复杂性. 为混沌序列在密码学和混沌保密通信中的应用提供了理论依据.To analyze the complexity of chaotic sequence correctly, complexity of systems, including typical discrete chaotic systems and continuous chaotic systems, are investigated based on the FuzzyEn algorithm. Compared with ApEn, SampEn and Intensive statistical complexity algorithm, the FuzzyEn algorithm is an effective measure algorithm for analyzing chaotic sequence complexity, and it has low sensitivity to and slight dependences on phase space dimension (m), similar tolerance (r) and sequence length (N), better robustness and measure value continuities. Results of the complexities of chaotic systems show that the complexity of continuous chaotic systems are much smaller than those of the discrete chaotic systems. However, having been disturbed by high complex discrete chaotic pseudo-random sequences or classical m-series, the pseudo-random sequences of continuous chaotic systems increase their complexities significantly. Our result provides a theoretical basis for the application of chaotic sequences to the field of cryptography and secure communication.
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Keywords:
- fuzzyEn /
- discrete chaotic system /
- continuous chaotic system /
- complexity
[1] Amig J M, Kocarev L, Szczepanski J 2006 Phys. Lett. A 355 27
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[6] Pincus S M 1995 Chaos 5 110
[7] [8] [9] Richman J S, Moorman J R 2000 Heart and Circulatory Physiology 278 2039
[10] Sun K H, He S B, Sheng L Y 2011 Acta Phys. Sin. 60 020505 (in Chinese) [孙克辉, 贺少波, 盛利元 2011 60 020505]
[11] [12] [13] 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 华南理工大学学报 38 18]
[14] [15] 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 53 2877]
[16] [17] Rajeev K Azad, J Subba Rao, Ramakrishna Ramaswamy 2002 Chaos 14 633
[18] [19] Chen W T, Wang Z Z, Xie H B, Yu W X 2007 IEEE Transactions on Neural Systems and Rehabilitation Engineering 15 266
[20] Chen W T, Zhuang J, Yu W X, Wang Z Z 2009 Medical Engineering and Physics 31 61
[21] [22] Chen X J, Li Z, Bai B M 2011 Journal of Electronics Information Technology 33 1198 (in Chinese) [陈小军, 李赞, 白宝明 2011 电子与信息学报 33 1198]
[23] [24] [25] 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 57 3359]
[26] Cai J P, Li Z, Song W T 2003 Acta Phys. Sin. 52 1871 (in Chinese) [蔡觉平, 李 赞, 宋文涛 2003 52 1871]
[27] [28] [29] Sun K H, Sprott J C 2009 International Journal of Nonlinear Sciences Numerical Simulation 10 1443
[30] Sun K H, Wang X 2010 International Journal of Bifurcation and Chaos 20 1209
[31] [32] [33] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 (in Chinese) [王兴元, 王明军 2007 56 5136]
[34] [35] 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 55 3964]
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[1] Amig J M, Kocarev L, Szczepanski J 2006 Phys. Lett. A 355 27
[2] [3] Huang L L, Yin Q T 2009 Journal of Electronics Information Technology 31 2402 (in Chinese) [黄丽莲, 尹启天 2009 电子与信息学报 31 2402]
[4] [5] Parlitz U, Ergezinger S 1994 Phys. Lett. A 188 146
[6] Pincus S M 1995 Chaos 5 110
[7] [8] [9] Richman J S, Moorman J R 2000 Heart and Circulatory Physiology 278 2039
[10] Sun K H, He S B, Sheng L Y 2011 Acta Phys. Sin. 60 020505 (in Chinese) [孙克辉, 贺少波, 盛利元 2011 60 020505]
[11] [12] [13] 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 华南理工大学学报 38 18]
[14] [15] 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 53 2877]
[16] [17] Rajeev K Azad, J Subba Rao, Ramakrishna Ramaswamy 2002 Chaos 14 633
[18] [19] Chen W T, Wang Z Z, Xie H B, Yu W X 2007 IEEE Transactions on Neural Systems and Rehabilitation Engineering 15 266
[20] Chen W T, Zhuang J, Yu W X, Wang Z Z 2009 Medical Engineering and Physics 31 61
[21] [22] Chen X J, Li Z, Bai B M 2011 Journal of Electronics Information Technology 33 1198 (in Chinese) [陈小军, 李赞, 白宝明 2011 电子与信息学报 33 1198]
[23] [24] [25] 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 57 3359]
[26] Cai J P, Li Z, Song W T 2003 Acta Phys. Sin. 52 1871 (in Chinese) [蔡觉平, 李 赞, 宋文涛 2003 52 1871]
[27] [28] [29] Sun K H, Sprott J C 2009 International Journal of Nonlinear Sciences Numerical Simulation 10 1443
[30] Sun K H, Wang X 2010 International Journal of Bifurcation and Chaos 20 1209
[31] [32] [33] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 (in Chinese) [王兴元, 王明军 2007 56 5136]
[34] [35] 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 55 3964]
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