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磁控二氧化钛忆阻混沌系统及现场可编程逻辑门阵列硬件实现

许雅明 王丽丹 段书凯

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磁控二氧化钛忆阻混沌系统及现场可编程逻辑门阵列硬件实现

许雅明, 王丽丹, 段书凯

A memristor-based chaotic system and its field programmable gate array implementation

Xu Ya-Ming, Wang Li-Dan, Duan Shu-Kai
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  • 忆阻器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, 减小系统的物理尺寸. 本文将磁控二氧化钛忆阻器应用到一个新的三维自治混沌系统中, 通过理论推导和数值仿真, 从平衡点的稳定性、 Lyapunov指数谱、庞加莱截面和功率谱等方面研究了该系统的动力学特性, 并详细讨论了不同参数变化对系统相图和平衡点稳定性的影响. 有趣的是, 在改变参数的情况下, 系统的吸引子会产生翻转、混沌程度加剧和混叠的现象, 说明该忆阻混沌系统具有丰富的动力学行为. 此外, 本文将改进的牛顿迭代法运用于现场可编程逻辑门阵列 技术中, 巧妙设计出一种只迭代3次就能达到所需精度的开方运算器, 从而硬件实现了该忆阻混沌系统. 这突破了以往忆阻器混沌系统只能在计算机模拟平台仿真的瓶颈, 为进一步研究忆阻混沌系统及其在保密通信、信息处理中的应用提供了参考.
    A nanoscale memristor can replace the nonlinear part of a chaotic system, which can greatly reduce the physical size of the chaotic system. More importantly, it can enhance the complexity of the chaotic system and the randomness of signals. In this paper, a new memristor-based chaotic system is designed based on a new three-dimensional autonomous chaotic system. In order to study the complex dynamic characteristics of the memristive system, the chaotic system is investigated by the theoretical derivation, numerical simulation, stabilization of equilibrium points, and Lyapunov exponent spectrum. The influences of different parameters on the phase diagram and the stability of equilibrium point of this system are also discussed in detail. It is interesting that when system parameters a and c take different values, the location and stability of the equilibrium point of the system will be changed, then two scrolls of the system will be overturned at a different angle, and it will produce a different degree of aliasing between the two scrolls. Parameter b has a large variable range, when it is changed, and the system will transform into three kinds of classical chaotic systems defined by Vaněček and Celikovsk. These indicate that the memristor-based chaotic system has a lot of valuable dynamic behaviors, so it has applications in the field of secure communication, information processing etc. Field programmable gate array (FPGA) technology has a large capacity and high reliability, which is widely used in modern digital signal processing. And with the development of FPGA technology, applying FPGA technology to realizing the chaotic systems has gradually become a hot topic. Moreover, the improved Newton iteration method is used to design a square root operator of memristor in this paper by using verilog hardware description language (verilog HDL) which only needs three times iteration to reach the required accuracy. The results of FPGA hardware are consistent with the numerical simulation results. It breaks through the previous bottleneck that the chaotic system based on titanium dioxide memristor can only be simulated in computer, which is of great significance for further studing of memristor, and provides a reference for further research on the memristor-based chaotic system and applications in secure communication and information processing.
      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, 61571372)、新世纪优秀人才支持计划(批准号: 教技函[2013]47号)和中央高校基本业务费专项资金 (批准号: XDJK2016A001, XDJK2014A009)资助的课题.
      Corresponding author: Wang Li-Dan, ldwang@swu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61372139, 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).
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    Chua L O 1971 IEEE Trans. Circ. Theor. 18 507

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    Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80

    [4]

    Kavehei O, Iqbal A, Kim Y S, Eshraghian K, Al-Sarawi S F, Abbott D 2010 Proc. R. Soc. A 466 2175

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    Biolek Z, Biolek D, Biolkov V 2009 Radio. Eng. 18 210

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    Jo S H, Kim K H, Lu W 2009 Nano Lett. 9 870

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    Yang J, Wang L D, Duan S K 2016 Sci. China Inf. Sci. 46 391

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    Wang L D, Li H F, Duan S K, Huang T W, Wang H M 2015 Neurocomputing 171 23

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    Hu X F, Chen G R, Duan S K, Feng G 2014 In Memristor Networks (Springer International Publishing) pp351-364

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    Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurcat. Chaos 22 1250205

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    Zhong G Q, Man K F, Chen G R 2002 Int. J. Bifurcat. Chaos 12 2907

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    Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Tech. Sci. 54 2180

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    Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502

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    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]

    [18]

    Li H F, Wang L D, Duan S K 2014 Int. J. Bifurcat. Chaos 24 7

    [19]

    Wang L D, Duan S K 2012 Abstr. Appl. Anal. 2012 2012

    [20]

    Li C L, Yu S M, Luo X S 2012 Acta Phys. Sin. 61 110502 (in Chinese) [李春来, 禹思敏, 罗晓曙 2012 物理学报 61 110502]

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    Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872

    [22]

    Wang Z L 2008 Comput. Eng. Appl. 44 84 (in Chinese) [王忠林 2008 计算机工程与应用 44 84]

    [23]

    Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 物理学报 63 060501]

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    Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi'an: Xi'an Electronic Sience and Technology University Press) pp126-148 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第126-148页]

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    Vaněčk A, Člikovsk S 1996 Control Systems: From Linear Analysis to Synthesis of Chaos (London: Prentice Hall International Ltd.) pp10-121

  • [1]

    Lorenz E N 1963 J. Atmos. Sci. 20 130

    [2]

    Chua L O 1971 IEEE Trans. Circ. Theor. 18 507

    [3]

    Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80

    [4]

    Kavehei O, Iqbal A, Kim Y S, Eshraghian K, Al-Sarawi S F, Abbott D 2010 Proc. R. Soc. A 466 2175

    [5]

    Biolek Z, Biolek D, Biolkov V 2009 Radio. Eng. 18 210

    [6]

    Pershin Y V, Di V M 2008 Phys. Rev. B 78 3309

    [7]

    Jo S H, Kim K H, Lu W 2009 Nano Lett. 9 870

    [8]

    Yang J, Wang L D, Duan S K 2016 Sci. China Inf. Sci. 46 391

    [9]

    Wang L D, Li H F, Duan S K, Huang T W, Wang H M 2015 Neurocomputing 171 23

    [10]

    Wang L D, Duan M T, Duan S K, Hu X F 2014 Sci. China Inf. Sci. 44 920

    [11]

    Hu X F, Chen G R, Duan S K, Feng G 2014 In Memristor Networks (Springer International Publishing) pp351-364

    [12]

    Muthuswamy B, Kokate P P 2009 IETE Tech. Rev. 26 417

    [13]

    Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurcat. Chaos 22 1250205

    [14]

    Zhong G Q, Man K F, Chen G R 2002 Int. J. Bifurcat. Chaos 12 2907

    [15]

    Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Tech. Sci. 54 2180

    [16]

    Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502

    [17]

    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]

    [18]

    Li H F, Wang L D, Duan S K 2014 Int. J. Bifurcat. Chaos 24 7

    [19]

    Wang L D, Duan S K 2012 Abstr. Appl. Anal. 2012 2012

    [20]

    Li C L, Yu S M, Luo X S 2012 Acta Phys. Sin. 61 110502 (in Chinese) [李春来, 禹思敏, 罗晓曙 2012 物理学报 61 110502]

    [21]

    Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872

    [22]

    Wang Z L 2008 Comput. Eng. Appl. 44 84 (in Chinese) [王忠林 2008 计算机工程与应用 44 84]

    [23]

    Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 物理学报 63 060501]

    [24]

    Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi'an: Xi'an Electronic Sience and Technology University Press) pp126-148 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第126-148页]

    [25]

    Vaněčk A, Člikovsk S 1996 Control Systems: From Linear Analysis to Synthesis of Chaos (London: Prentice Hall International Ltd.) pp10-121

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出版历程
  • 收稿日期:  2016-02-17
  • 修回日期:  2016-04-01
  • 刊出日期:  2016-06-05

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