基于忆阻器的时滞混沌系统及伪随机序列发生器

吴洁宁; 王丽丹; 段书凯

doi:10.7498/aps.66.030502

摘要

忆阻器作为可调控的非线性元件，很容易实现混沌信号的产生.基于忆阻器的混沌系统是当下研究的热点，但是基于忆阻器的时滞混沌系统目前却鲜有人涉足.因此，本文提出了一个新型忆阻时滞混沌系统.时延的存在增加了系统的复杂性，使系统能够产生更丰富、更复杂的动力学行为.我们对提出的忆阻时滞混沌系统进行了稳定性分析，确定了显示系统稳定平衡点的相应参数区域.讨论了在不同参数情况下的系统状态，系统呈现出形态各异的混沌吸引子相图，表现出丰富的混沌特性和非线性特性.最后，将系统用于产生伪随机序列，并经过实验验证，我们提出的系统具有良好的自相关性和互相关性，同时能获得相对显著的近似熵.该时滞混沌系统具有复杂的动力学行为和良好的随机性，能满足扩频通信和图像加密等众多领域的应用需要.

关键词:

Abstract

Memristor, a controllable nonlinear element, is easy to generate a chaotic signal. More significantly, it can improve the complexity of the chaotic system and the randomness of signals. Although the memristor chaotic system is a hot spot of research currently, little attention has been paid to the memristive time-delayed chaotic system. Therefore, a new memristor-based time-delayed chaotic system is proposed in this paper. We construct the time-delayed chaotic system with single delay time by using the nonlinear relationship between the memristance and charge of memristor. The existence of time delay enhances the complexity of chaotic system, which makes the system produce richer and more complex dynamics. In order to study the complex dynamic characteristics of this memristive time-delayed system, we investigate the proposed system by theoretical derivation, numerical simulation, stabilization of equilibrium points, and power spectrum. In addition, the corresponding parameter region of the stable equilibrium point of the system is discussed in detail. Then, we discuss the effect of parameter variation on the dynamic behavior of the system, and a series of phase diagrams with different time-delayed parameters and system parameters is described by numerical simulation. We find that different combinations of parameters and slight changes of parameters can make the system a completely different phase diagram, which indicates that the proposed system has rich nonlinear characteristic. Moreover, the proposed time-delayed system is used to generate pseudo random sequences, and the experimental results show that the proposed system has good self-correlation, cross-correlation, and the significant approximate entropy. According to the theoretical analyses and experimental results, we conclude that the proposed new time-delayed chaotic system has complex dynamic behavior and good randomness, which can meet the needs of the applications in spread spectrum communication, image encryption and many other fields. This research provides a significant reference for further studying the usage of memristor.

Keywords:

作者及机构信息

1.
西南大学电子信息工程学院, 重庆 400715;

2.
非线性电路与智能信息处理重庆市重点实验室, 重庆 400715

通信作者: 王丽丹, ldwang@swu.edu.cn

基金项目: 国家自然科学基金（批准号：61372139，61672436，61571372）、新世纪优秀人才支持计划（批准号：教技函[2013]47号）和中央高校基本科研业务费专项资金（批准号：XDJK2016A001，XDJK2014A009）资助的课题.

Authors and contacts

1.
School of Electronic and Information Engineering, Southweat University, Chongqing 400715, China;

2.
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing 400715, China

Corresponding author: Wang Li-Dan, ldwang@swu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61372139, 61672436, 61571372), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No.[2013]47), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. XDJK2016A001, XDJK2014A009).

参考文献

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[4]	Jo S H, Chang T, Ebong I, Bhadviya B B, Mazumder P, Lu W 2010 Nano Lett. 10 1297
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[6]	Wang L D, Li H F, Duan S K, Huang T W, Wang H M 2016 Neurocomputing 171 23
[7]	Sah M P, Yang C, Kim H, Chua L 2012 Sensors 12 3587
[8]	Hu X F, Chen G R, Duan S K, Feng G 2014 In Memristor Networks (Springer International Publishing) pp351-364
[9]	Itoh M, Chua L O 2008 Int. J. Bifurcat. Chaos 18 3183
[10]	Muthuswamy B, Kokate P P 2009 IETE Tech. Rev. 26 417
[11]	Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 228
[12]	Min G Q, Wang L D, Duan S K 2015 Acta Phys. Sin. 64 210507 (in Chinese)[闵国旗, 王丽丹, 段书凯2015 64 210507]
[13]	Stork M, Hrusak J, Mayer D 2009 International Conference on Electrical and Electronics Engineering, 2009 ELECO Bursa, Turkey, November 5-8, 2009 pp58-60
[14]	Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurcat. Chaos 22 1250205
[15]	Li H F, Wang L D, Duan S K 2014 Int. J. Bifurcat. Chaos 24 1450099
[16]	Cafagna D, Grassi G 2012 Nonlinear Dyn. 70 1185
[17]	Yang Y F, Leng J L, Li Q D 2014 Acta Phys. Sin. 63 080502 (in Chinese)[杨芳艳, 冷家丽, 李清都2014 63 080502]
[18]	Mackey M C, Glass L 1977 Science 197 287
[19]	Lakshmanan M, Senthilkumar D V 2011 Dynamics of Nonlinear Time-Delay Systems (Springer Science & Business Media Press) pp27-36
[20]	Ikeda K, Daido H, Akimoto O 1980 Phys. Rev. Lett. 45 709
[21]	Boutle I, Taylor R H S, Römer R A 2007 Am. J. Phys. 75 15
[22]	Wu F X 2009 Adv. Complex Syst. 12 3
[23]	Liao X X, Chen G R 2003 Int. J. Bifurcat. Chaos 13 207
[24]	Lu J Q, Cao J D, Ho D W C 2008 IEEE Trans. Circuits Syst. I, Reg. Papers 55 1347
[25]	Zhang X M, Chen J F, Peng J H 2011 Int. J. Bifurcat. Chaos 21 2547
[26]	Guan G R, Wu C M, Jia Q 2015 Acta Phys. Sin. 64 020501 (in Chinese)[官国荣, 吴成茂, 贾倩2015 64 020501]

施引文献

[1]	Chua L O 1971 IEEE Trans. Circ. Theor. 18 507
[2]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[3]	Corinto F, Ascoli A, Gilli M 2011 IEEE Trans. Circuits Syst. I, Reg. Papers. 58 1323
[4]	Jo S H, Chang T, Ebong I, Bhadviya B B, Mazumder P, Lu W 2010 Nano Lett. 10 1297
[5]	Yang J J, Pickett M D, Li X, Ohlberg D A, Stewart D R, Williams R S 2008 Nat. Nanotech. 3 429
[6]	Wang L D, Li H F, Duan S K, Huang T W, Wang H M 2016 Neurocomputing 171 23
[7]	Sah M P, Yang C, Kim H, Chua L 2012 Sensors 12 3587
[8]	Hu X F, Chen G R, Duan S K, Feng G 2014 In Memristor Networks (Springer International Publishing) pp351-364
[9]	Itoh M, Chua L O 2008 Int. J. Bifurcat. Chaos 18 3183
[10]	Muthuswamy B, Kokate P P 2009 IETE Tech. Rev. 26 417
[11]	Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 228
[12]	Min G Q, Wang L D, Duan S K 2015 Acta Phys. Sin. 64 210507 (in Chinese)[闵国旗, 王丽丹, 段书凯2015 64 210507]
[13]	Stork M, Hrusak J, Mayer D 2009 International Conference on Electrical and Electronics Engineering, 2009 ELECO Bursa, Turkey, November 5-8, 2009 pp58-60
[14]	Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurcat. Chaos 22 1250205
[15]	Li H F, Wang L D, Duan S K 2014 Int. J. Bifurcat. Chaos 24 1450099
[16]	Cafagna D, Grassi G 2012 Nonlinear Dyn. 70 1185
[17]	Yang Y F, Leng J L, Li Q D 2014 Acta Phys. Sin. 63 080502 (in Chinese)[杨芳艳, 冷家丽, 李清都2014 63 080502]
[18]	Mackey M C, Glass L 1977 Science 197 287
[19]	Lakshmanan M, Senthilkumar D V 2011 Dynamics of Nonlinear Time-Delay Systems (Springer Science & Business Media Press) pp27-36
[20]	Ikeda K, Daido H, Akimoto O 1980 Phys. Rev. Lett. 45 709
[21]	Boutle I, Taylor R H S, Römer R A 2007 Am. J. Phys. 75 15
[22]	Wu F X 2009 Adv. Complex Syst. 12 3
[23]	Liao X X, Chen G R 2003 Int. J. Bifurcat. Chaos 13 207
[24]	Lu J Q, Cao J D, Ho D W C 2008 IEEE Trans. Circuits Syst. I, Reg. Papers 55 1347
[25]	Zhang X M, Chen J F, Peng J H 2011 Int. J. Bifurcat. Chaos 21 2547
[26]	Guan G R, Wu C M, Jia Q 2015 Acta Phys. Sin. 64 020501 (in Chinese)[官国荣, 吴成茂, 贾倩2015 64 020501]

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