A novel method of constructing high-dimensional digital chaotic systems on finite-state automata

doi:10.1088/1674-1056/aba60f

中国物理B ›› 2020, Vol. 29 ›› Issue (9): 90502-090502.doi: 10.1088/1674-1056/aba60f

A novel method of constructing high-dimensional digital chaotic systems on finite-state automata

Jun Zheng(郑俊), Han-Ping Hu(胡汉平)

1 School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China;
2 Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education, Wuhan 430074, China

收稿日期:2020-05-18 修回日期:2020-07-07 接受日期:2020-07-15 出版日期:2020-09-05 发布日期:2020-09-05
通讯作者: Han-Ping Hu E-mail:husthhh@qq.com
基金资助:
Project supported by the National Key R&D Program of China (Grant No. 2017YFB0802000) and the Cryptography Theoretical Research of National Cryptography Development Fund, China (Grant No. MMJJ20170109).

A novel method of constructing high-dimensional digital chaotic systems on finite-state automata

Jun Zheng(郑俊)¹, Han-Ping Hu(胡汉平)^1,2

1 School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China;
2 Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education, Wuhan 430074, China

Received:2020-05-18 Revised:2020-07-07 Accepted:2020-07-15 Online:2020-09-05 Published:2020-09-05
Contact: Han-Ping Hu E-mail:husthhh@qq.com
Supported by:
Project supported by the National Key R&D Program of China (Grant No. 2017YFB0802000) and the Cryptography Theoretical Research of National Cryptography Development Fund, China (Grant No. MMJJ20170109).

摘要/Abstract

摘要： When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical degradation of low-dimensional chaotic maps. This paper presents a novel method to construct high-dimensional digital chaotic systems in the domain of finite computing precision. The model is proposed by coupling a high-dimensional digital system with a continuous chaotic system. A rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney's definition of chaos. Numerical experimental results for different high-dimensional digital systems indicate that the proposed method can overcome the degradation problem and construct high-dimensional digital chaos with complicated dynamical properties. Based on the construction method, a kind of pseudorandom number generator (PRNG) is also proposed as an application.

关键词: high-dimensional digital chaotic system, dynamical degradation, anti-control, pseudorandom number generator

Abstract: When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical degradation of low-dimensional chaotic maps. This paper presents a novel method to construct high-dimensional digital chaotic systems in the domain of finite computing precision. The model is proposed by coupling a high-dimensional digital system with a continuous chaotic system. A rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney's definition of chaos. Numerical experimental results for different high-dimensional digital systems indicate that the proposed method can overcome the degradation problem and construct high-dimensional digital chaos with complicated dynamical properties. Based on the construction method, a kind of pseudorandom number generator (PRNG) is also proposed as an application.

Key words: high-dimensional digital chaotic system, dynamical degradation, anti-control, pseudorandom number generator

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

05.45.Gg (Control of chaos, applications of chaos) 05.45.Jn (High-dimensional chaos) 05.45.Vx (Communication using chaos)

郑俊, 胡汉平. A novel method of constructing high-dimensional digital chaotic systems on finite-state automata[J]. 中国物理B, 2020, 29(9): 90502-090502.

Jun Zheng(郑俊), Han-Ping Hu(胡汉平). A novel method of constructing high-dimensional digital chaotic systems on finite-state automata[J]. Chin. Phys. B, 2020, 29(9): 90502-090502.

参考文献 31

[1]	Motter A E and Campbell D K 2013 Phys. Today 66 27
[2]	Li T Y and Yorke J A 1975 Am. Math. Mon. 82 985 doi: 10.1080/00029890.1975.11994008
[3]	Alvarez G and Li S 2006 Int. J. Bifurcation Chaos 16 2129 doi: 10.1142/S0218127406015970
[4]	Millerioux G, Amigo J M, Daafouz J, et al. 2008 IEEE Trans. Circuits Syst. I-Regul. Pap. 55 1695 doi: 10.1109/TCSI.2008.916555
[5]	Ozkaynak F 2018 Nonlinear Dyn. 92 305 doi: 10.1007/s11071-018-4056-x
[6]	Yin R, Wang J, Yuan J, et al. 2012 Sci. Chin. Inf. Sci. 55 1162 doi: 10.1007/s11432-011-4401-x
[7]	Gao X J, Cheng M F, Deng L, et al. 2020 Opt. Express 28 10847 doi: 10.1364/OE.389251
[8]	Ozkaynak F 2014 Nonlinear Dyn. 78 2015 doi: 10.1007/s11071-014-1591-y
[9]	Li S, Chen G, Mou X, et al. 2005 Int. J. Bifurcation Chaos 15 3119 doi: 10.1142/S0218127405014052
[10]	Kwok H S and Tang W K 2007 Chaos Solitons Fractal 32 1518 doi: 10.1016/j.chaos.2005.11.090
[11]	Yang B and Liao X 2017 Sci. Chin. Inf. Sci. 60 022302 doi: 10.1007/s11432-015-0756-1
[12]	Liu L, Lin J, Miao S, et al. 2017 Int. J. Bifurcation Chaos 27 1750103 doi: 10.1142/S0218127417501036
[13]	Wang C and Ding Q 2019 Complexity 2019 5942121
[14]	Liu H, Zhang Y, Kadir A, et al. 2019 Appl. Math. Comput. 360 83
[15]	Alawida M, Samsudin A, Teh J S, et al. 2019 Signal Process 160 45 doi: 10.1016/j.sigpro.2019.02.016
[16]	Antonelli M, De Micco L, Larrondo H A, et al. 2018 Entropy 20 135 doi: 10.3390/e20020135
[17]	Sun C C, Xu Q C and Sui Y 2013 Chin. Phys. B 22 030507 doi: 10.1088/1674-1056/22/3/030507
[18]	Hu H, Xu Y and Zhu Z 2008 Chaos Solitons Fractal. 38 439 doi: 10.1016/j.chaos.2006.11.027
[19]	Tutueva A V, Andreev V S, Karimov A I, et al. 2020 Chaos Solitons Fractals. 133 109615 doi: 10.1016/j.chaos.2020.109615
[20]	Moysis L, Tutueva A, Volos C, et al. 2020 Symmetry 12 829 doi: 10.3390/sym12050829
[21]	Guyeux C and Bahi J M 2010 International Joint Conference on neural network (IJCNN), July 18-23, 2010, Barcelona, Spain, pp. 1-7
[22]	Wang Q, Yu S, Guyeux C, et al. 2014 Int. J. Bifurcation Chaos 24 1450128 doi: 10.1142/S0218127414501284
[23]	Wang Q, Yu S, Guyeux C, et al. 2015 Chin. Phys. B 24 060503 doi: 10.1088/1674-1056/24/6/060503
[24]	Alawida M, Teh J S, Samsudin A, et al. 2019 Signal Process. 164 249 doi: 10.1016/j.sigpro.2019.06.013
[25]	Alawida M, Samsudin A, Teh J S, et al. 2019 Nonlinear Dyn. 98 2403 doi: 10.1007/s11071-019-05311-z
[26]	Zheng J, Hu H, Ming H, et al. 2020 Chaos Solitons Fractals 138 109863 doi: 10.1016/j.chaos.2020.109863
[27]	Lv X, Liao X, Yang B, et al. 2018 Nonlinear Dyn. 94 325 doi: 10.1007/s11071-018-4361-4
[28]	Fu C, Wen Z K, Zhu Z L, et al. 2016 Int. J. Comput. Sci. Eng. 12 113
[29]	Banks J, Brooks J, Cairns G, et al. 1992 Am. Math. Mon 99 332 doi: 10.1080/00029890.1992.11995856
[30]	Marwan N, Romano M C, Thiel M, et al. 2007 Phys. Rep. 438 237 doi: 10.1016/j.physrep.2006.11.001
[31]	Pincus S M 1991 Proc. Nat Acad. Sci. USA 88 2297 doi: 10.1073/pnas.88.6.2297

A novel method of constructing high-dimensional digital chaotic systems on finite-state automata

A novel method of constructing high-dimensional digital chaotic systems on finite-state automata

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