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忆阻器是一种具有记忆功能和纳米级尺寸的非线性元件，作为混沌系统的非线性部分，能够提高混沌系统的信号随机性和复杂度.本文基于增广L系统设计了一个三维忆阻混沌系统.仅仅通过改变系统的一个参数，该系统能产生单涡巻、双涡卷和四涡巻的混沌吸引子，说明该系统具有丰富的混沌特性.首先对该忆阻混沌系统的基本动力学行为进行了理论分析和数值仿真，如平衡点稳定性、对称性，Lyapunov指数和维数，分岔图和Poincare截面等.同时，建立了模拟该忆阻混沌系统的SPICE（simulation program with integrated circuit emphasis）电路，给出了不同参数下的电路实验相图，其仿真结果与数值分析相符，从而验证了该忆阻混沌系统的混沌产生能力.由于脉冲同步只在离散时刻传递信息，能量消耗小，同步速度快，易于实现单信道传输，因而在混沌保密通信中更具有实用性.因此，本文从最大Lyapunov指数的角度实现了该忆阻混沌系统的脉冲混沌同步，数值仿真证实了忆阻混沌系统的存在性以及脉冲同步控制的可行性，为进一步研究该忆阻混沌系统在语音保密通信和信息处理中的应用提供了实验基础.The memristor is a nonlinear element and intrinsically possesses memory function. When it works as nonlinear part of a chaotic system, the complexity and the randomness of signal will be enhanced. In this paper memristor is introduced into a three-dimensional chaotic system based on the augmented L system. The interesting and promising behaviors of complex single, double and four-scroll chaotic attractors generated only by varying a parameter have not been reported in memristive chaotic system and thus they deserve to be further investigated. It is also obvious that such a simple change of one parameter could be used to generate a variety of quite complex attractors. Therefore, as a nonlinear device the memristor plays an important role in this system. Firstly, some basic dynamical properties of the memristive chaotic system, including symmetry and in-variance, the existence of attractor, equilibrium, and stability are investigated in detail. By numerically simulating the power spectrum, Lyapunov exponent, Poincare map and bifurcation diagram, in this paper we verify that the proposed system has abundant dynamical behaviors. The sensitivities of system parameters to the chaotic behaviors are further explored by calculating, in detail, its Lyapunov exponent spectrum and bifurcation diagrams. The results of simulation and experiment are in good agreement, thereby proving the veracity of analysis. The memristive chaotic circuit is designed using the memristor, operational amplifier, analog multiplier and other conventional components. The circuit implementation of the memristive system is simulated using SPICE (simulation program with integrated circuit emphasis). The SPICE simulation results and the theoretical analysis are found to be in good agreement, and thus verifying that the system can produce chaos. Pulse synchronization has the following characteristics: low energy consumption, fast synchronization and easy-to-implement single-channel transmission. Therefore, it is more practical in chaotic secure communication. Subsequently the pulse chaos synchronization is realized from the perspective of the maximum Lyapunov exponent, and numerical simulations show the existence of new memristive chaotic system and the feasibility of pulse synchronization control, and also provide an experimental basis for further studying the applications of the memristive chaotic system in voice secure communication and information processing.
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Keywords:
- memristor /
- chaotic attractors /
- SPICE design /
- the pulse synchronous control
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[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 83
[3] Tour J M, He T 2008 Nature 453 42
[4] Yang Y C, Pan F, Liu Q, Liu M, Zeng F 2009 Nano Lett. 9 1636
[5] Pershin Y V, Di Ventra M 2010 Neural Netw. 23 881
[6] Pershin Y V, Fontaine S L, Di Ventra M 2010 Neural Netw. 23 881
[7] Wang L D, Li H F, Duan S K, Huang T W 2016 Neurocomputing 171 23
[8] Wang H M, Duan S K, Huang T W, Wang L D, Li C D 2017 IEEE Trans. Neur. Net. Lear. 28 766
[9] Shin S, Kim K, Kang S M 2011 IEEE Trans. Nanotechnol. 10 266
[10] Witrisal K 2009 Electron. Lett. 45 713
[11] Itoh M, Chua L O 2008 Int. J. Bifurcat. Chaos 18 3183
[12] Bharathwaj M, Kokate P P 2009 IETE Tech. Rev. 26 415
[13] Muthuswamy B 2010 Int. J Bifurcat. Chaos 20 1335
[14] Bao B C, Xu J P, Zhou G H, Liu Z 2011 Chin. Phys. B 20 109
[15] Bao B C, Xu J P, Liu Z 2010 Chin. Phys. Lett. 27 51
[16] Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 237
[17] Wang L D, Duan S K, Drakakis E, He P F, Liao X F 2012 Int. J. Bifurcat. Chaos 22 241
[18] Iu H H C, Yu D S, Fitch A L, Chen H 2011 IEEE Trans. Circ. Syst. I 58 1337
[19] Wang W, Zeng Y C, Sun R T 2017 Acta Phys. Sin. 66 040502(in Chinese) [王伟, 曾以成, 孙睿婷 2017 物理学报 66 040502]
[20] Ruan J Y, Sun K H, Mou J 2016 Acta Phys. Sin. 65 190502(in Chinese) [阮静雅, 孙克辉, 牟俊 2016 物理学报 65 190502]
[21] Joglekar Y N, Wolf S J 2009 Eur.J. Phys. 30 661
[22] Xu Y M, Wang L D, Duan S K 2016 Acta Phys. Sin. 65 120503(in Chinese) [许雅明, 王丽丹, 段书凯 2016 物理学报 65 120503]
[23] 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 物理学报 64 210507]
[24] Wu J N, Wang L D, Chen G R, Duan S K 2016 Chaos, Solitons Fract. 92 20
[25] Min G Q, Wang L D, Duan S K 2016 Int. J. Bifurcat. Chaos 26 1650129
[26] Wang X Y 2012 Synchronization of Chaotic System and Its Application in Secure Communication (Beijing: The Science Press) pp173-187 (in Chinese) [王兴元 2012 混沌系统的同步及在保密通信中的应用(北京: 科学出版社) 第173187页]
[27] Itoh M, Yang T, Chua L O 2001 Int. J. Bifurcat. Chaos 11 551
[28] Li C D, Liao X F 2004 Chaos, Solitons Fract. 22 857
[29] Wang Y W, Guan Z H, Xiao J 2004 Chaos 14 199
[30] Ren Q S, Zhao J Y 2006 Phys. Lett. A 355 342
[31] L J H, Chen G R 1999 Int. J. Bifurcat. Chaos 9 1420
[32] L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Its Application (Wuhan: The Wuhan University Press) pp176-177 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉：武汉大学出版社) 第176177页]
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