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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
[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 55 3964]
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