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Memristor-based multi-scroll chaotic system and its pulse synchronization control

Yan Deng-Wei Wang Li-Dan Duan Shu-Kai

Memristor-based multi-scroll chaotic system and its pulse synchronization control

Yan Deng-Wei, Wang Li-Dan, Duan Shu-Kai
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  • 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.
      Corresponding author: Wang Li-Dan, ldwang@swu.edu.cn
    • Funds: Project supported by the National Natural Science of China (Grant Nos. 61571372, 61672436), the Fundamental Research Funds for the Central Universities, China (Grant Nos. XDJK2016A001, XDJK2017A005), and the Chongqing Basic Science and Frontier Technology Research, China (Grant No. cstc2017jcyjBX0050).
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    [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]

  • [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]

  • [1] Li Zhi-Jun, Zeng Yi-Cheng, Li Zhi-Bin. Memristive chaotic circuit based on modified SC-CNNs. Acta Physica Sinica, 2014, 63(1): 010502. doi: 10.7498/aps.63.010502
    [2] Ruan Jing-Ya, Sun Ke-Hui, Mou Jun. Memristor-based Lorenz hyper-chaotic system and its circuit implementation. Acta Physica Sinica, 2016, 65(19): 190502. doi: 10.7498/aps.65.190502
    [3] Wang Wei, Zeng Yi-Cheng, Sun Rui-Ting. Research on a six-order chaotic circuit with three memristors. Acta Physica Sinica, 2017, 66(4): 040502. doi: 10.7498/aps.66.040502
    [4] Bao Bo-Cheng, Hu Wen, Xu Jian-Ping, Liu Zhong, Zou Ling. Analysis and implementation of memristor chaotic circuit. Acta Physica Sinica, 2011, 60(12): 120502. doi: 10.7498/aps.60.120502
    [5] Wang De-Chun, Li Chun-Biao. An attractor with invariable Lyapunov exponent spectrum and its Jerk circuit implementation. Acta Physica Sinica, 2009, 58(2): 764-770. doi: 10.7498/aps.58.764
    [6] Yang Fang-Yan, Leng Jia-Li, Li Qing-Du. The 4-dimensional hyperchaotic memristive circuit based on Chua’s circuit. Acta Physica Sinica, 2014, 63(8): 080502. doi: 10.7498/aps.63.080502
    [7] Hong Qing-Hui, Li Zhi-Jun, Zeng Jin-Fang, Zeng Yi-Cheng. Design and simulation of a memristor chaotic circuit based on current feedback op amp. Acta Physica Sinica, 2014, 63(18): 180502. doi: 10.7498/aps.63.180502
    [8] Li Chun-Biao, Wang Han-Kang, Chen Su. A novel chaotic attractor with constant Lyapunov exponent spectrum and its circuit implementation. Acta Physica Sinica, 2010, 59(2): 783-791. doi: 10.7498/aps.59.783
    [9] Wu Jie-Ning, Wang Li-Dan, Duan Shu-Kai. A memristor-based time-delay chaotic systems and pseudo-random sequence generator. Acta Physica Sinica, 2017, 66(3): 030502. doi: 10.7498/aps.66.030502
    [10] Xu Bi-Rong. A simplest parallel chaotic system of memristor. Acta Physica Sinica, 2013, 62(19): 190506. doi: 10.7498/aps.62.190506
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Publishing process
  • Received Date:  03 January 2018
  • Accepted Date:  19 February 2018
  • Published Online:  05 June 2018

Memristor-based multi-scroll chaotic system and its pulse synchronization control

    Corresponding author: Wang Li-Dan, ldwang@swu.edu.cn
  • 1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing 400715, China;
  • 2. School of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
Fund Project:  Project supported by the National Natural Science of China (Grant Nos. 61571372, 61672436), the Fundamental Research Funds for the Central Universities, China (Grant Nos. XDJK2016A001, XDJK2017A005), and the Chongqing Basic Science and Frontier Technology Research, China (Grant No. cstc2017jcyjBX0050).

Abstract: 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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