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For any digital chaotic sequence generator, evaluating periodic characteristics which exist in only part of domains of binary chaotic sequences is extremely difficult. In this paper, we present a method which we name the binary sequence period detection (BSPD). The BSPD is a novel detection which evaluates the periodicity in a binary chaotic sequence, by which both the accurate-periodic phenomena and periodic phenomena in part of domains can be detected. Moreover, any periodic phenomenon pattern of a binary sequence can be located by the BSPD method. The experimental results show that the BSPD can detect and extract the periodic phenomena of the classical Logistic chaotic sequence generators.
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Keywords:
- chaos /
- binary sequences /
- period phenomena /
- detection
[1] Jakimoski G, Kocarev L 2001 IEEE Trans. Circuits and Systems I 48 163
[2] Kocarev L 2001 IEEE Circuits and Systems Magazine 1 6
[3] Baptista M S 1998 Phys. Lett. A 240 50
[4] Kohda T 2002 Proceedings IEEE 90 641
[5] Masuda N, Aihara K 2002 IEEE Trans. Circuits and Systems I 49 28
[6] Mazzini G, Setti G, Rovatti R 1997 IEEE Trans. Circuits and Systems I 44 937
[7] Liao N H, Gao J F 2006 J. Elec. Inf. Tech. 28 1255 (in Chinese) [廖旎焕, 高金峰 2006 电子与信息学报 28 1255]
[8] Wu H, Ding Q, Zhou P 2009 CIMCTC' 2012 Harbin, July 23-26 2009, pp372-375 (in Chinese) [巫红, 丁群, 周平 2009 中国仪器仪表与测控技术大会, 哈尔滨, 2009年7月23—26日, pp372-375]
[9] Van Wiggeren G D, Roy R 1998 Science 279 1198
[10] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[11] Cuomo K M, Oppenheim A V 1993 Phys. Rev. Lett. 71 65
[12] Kocarev L, Parlitz U 1995 Phys. Rev. Lett. 74 5028
[13] Boccaletti S, Kurths J Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1
[14] Ruelle D 1989 Chaotic Evolution and Strange Attractors: the Statistical Analysis of Time Series for Deterministic Nonlinear Systems (New York: Cambridge University Press) pp28-33
[15] Sang T, Wang R L, Yan Y X 2001 IEEE Trans. Commun. 49 620
[16] Kanso A, Smaoui N 2009 Chaos, Solitons and Fractals 40 2557
[17] Jiang H Y, Fu C A 2008 Proceedings of 2008 International Conference on Intelligent Computation Technology and Automation (Vol. 2) Changsha, October 20-22 2008 pp60-64
[18] Chen S L, Hwang T T, Lin W W 2010 IEEE Trans. Circuits and Systems II 57 996
[19] Kohda T, Tsuneda A 1997 IEEE Trans. Information Theory 43 104
[20] L'Ecuyer P 2006 Handbooks in Operations Research and Management Science: Simulation (Amsterdam: Elsevier B V) pp55-81
[21] James F 1990 Comput. Phys. Commun. 60 329
[22] Bresten C L, Jung J H 2009 Communications in Nonlinear Science and Numerical Simulation 14 3076
[23] Cheng L Y, Quan J B 2010 J. Comut. Appl. 30 1802 (in Chinese) [盛利元, 全俊斌 2010 计算机应用 30 1802]
[24] Fan J L, Zhang X F 2009 Acta Electron. Sin. 4 720 (in Chinese) [范九伦, 张雪峰 2009 电子学报 4 720]
[25] Kohda T, Tsuneda A 1993 IEICE Trans. Commun. E 76_B 855
[26] Liu N S H 2011 Communications in Nonlinear Science and Numerical Simulation 16 761
[27] Tsuneda A 2005 IEEE Trans. Circuits and Systems I 52 454
[28] Jessa M 2002 IEEE Trans. Circuits and Systems I 49 84
[29] Kleiner B 1977 Technometrics 19 343
[30] Rukhin A, Soto J, Nechvatal J, Smid M, Barker E, Leigh S, Levenson M, Vangel M, Banks D, Heckert A, Dray J, Vo S 2001 A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (Gaithersburg, MD, USA: NIST) p1, pp18-21
[31] L'Ecuyer P, Simard R 2007 ACM Trans. Math Software 33 1
[32] McCullough B D 2006 J. Appl. Econ. 21 677
[33] Xiang F, Qiu S S 2008 IEEE Commun. Lett. 12 337
[34] Zhang S R, Mei W H, Wang T C, Deng X Y 2000 Journal of China Institute of Communications 21 45 (in Chinese) [张申如, 梅文华, 王庭昌, 邓晓燕 2000 通信学报 21 45]
[35] Li C Y, Chen Y H, Chang T Y, Deng L Y, Kiwing T 2012 IEEE Trans. VLSI Systems 20 385
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[1] Jakimoski G, Kocarev L 2001 IEEE Trans. Circuits and Systems I 48 163
[2] Kocarev L 2001 IEEE Circuits and Systems Magazine 1 6
[3] Baptista M S 1998 Phys. Lett. A 240 50
[4] Kohda T 2002 Proceedings IEEE 90 641
[5] Masuda N, Aihara K 2002 IEEE Trans. Circuits and Systems I 49 28
[6] Mazzini G, Setti G, Rovatti R 1997 IEEE Trans. Circuits and Systems I 44 937
[7] Liao N H, Gao J F 2006 J. Elec. Inf. Tech. 28 1255 (in Chinese) [廖旎焕, 高金峰 2006 电子与信息学报 28 1255]
[8] Wu H, Ding Q, Zhou P 2009 CIMCTC' 2012 Harbin, July 23-26 2009, pp372-375 (in Chinese) [巫红, 丁群, 周平 2009 中国仪器仪表与测控技术大会, 哈尔滨, 2009年7月23—26日, pp372-375]
[9] Van Wiggeren G D, Roy R 1998 Science 279 1198
[10] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[11] Cuomo K M, Oppenheim A V 1993 Phys. Rev. Lett. 71 65
[12] Kocarev L, Parlitz U 1995 Phys. Rev. Lett. 74 5028
[13] Boccaletti S, Kurths J Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1
[14] Ruelle D 1989 Chaotic Evolution and Strange Attractors: the Statistical Analysis of Time Series for Deterministic Nonlinear Systems (New York: Cambridge University Press) pp28-33
[15] Sang T, Wang R L, Yan Y X 2001 IEEE Trans. Commun. 49 620
[16] Kanso A, Smaoui N 2009 Chaos, Solitons and Fractals 40 2557
[17] Jiang H Y, Fu C A 2008 Proceedings of 2008 International Conference on Intelligent Computation Technology and Automation (Vol. 2) Changsha, October 20-22 2008 pp60-64
[18] Chen S L, Hwang T T, Lin W W 2010 IEEE Trans. Circuits and Systems II 57 996
[19] Kohda T, Tsuneda A 1997 IEEE Trans. Information Theory 43 104
[20] L'Ecuyer P 2006 Handbooks in Operations Research and Management Science: Simulation (Amsterdam: Elsevier B V) pp55-81
[21] James F 1990 Comput. Phys. Commun. 60 329
[22] Bresten C L, Jung J H 2009 Communications in Nonlinear Science and Numerical Simulation 14 3076
[23] Cheng L Y, Quan J B 2010 J. Comut. Appl. 30 1802 (in Chinese) [盛利元, 全俊斌 2010 计算机应用 30 1802]
[24] Fan J L, Zhang X F 2009 Acta Electron. Sin. 4 720 (in Chinese) [范九伦, 张雪峰 2009 电子学报 4 720]
[25] Kohda T, Tsuneda A 1993 IEICE Trans. Commun. E 76_B 855
[26] Liu N S H 2011 Communications in Nonlinear Science and Numerical Simulation 16 761
[27] Tsuneda A 2005 IEEE Trans. Circuits and Systems I 52 454
[28] Jessa M 2002 IEEE Trans. Circuits and Systems I 49 84
[29] Kleiner B 1977 Technometrics 19 343
[30] Rukhin A, Soto J, Nechvatal J, Smid M, Barker E, Leigh S, Levenson M, Vangel M, Banks D, Heckert A, Dray J, Vo S 2001 A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (Gaithersburg, MD, USA: NIST) p1, pp18-21
[31] L'Ecuyer P, Simard R 2007 ACM Trans. Math Software 33 1
[32] McCullough B D 2006 J. Appl. Econ. 21 677
[33] Xiang F, Qiu S S 2008 IEEE Commun. Lett. 12 337
[34] Zhang S R, Mei W H, Wang T C, Deng X Y 2000 Journal of China Institute of Communications 21 45 (in Chinese) [张申如, 梅文华, 王庭昌, 邓晓燕 2000 通信学报 21 45]
[35] Li C Y, Chen Y H, Chang T Y, Deng L Y, Kiwing T 2012 IEEE Trans. VLSI Systems 20 385
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