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在提出的一种压控忆阻器的基础上, 构造了最简的并联忆阻器混沌系统, 分析其动力学特性, 得到了该系统的Lyapunov指数和Lyapunov维数, 给出了时域波形、相图、Lyapunov指数谱、分岔图、Poincar映射等. 利用EWB软件设计了该新混沌系统的振荡电路并进行了仿真实验. 研究结果表明, 忆阻器的i-v特性在参数的变化时, 并不保持斜8字形, 会变为带尾巴的扇形. 该混沌系统与磁控忆阻器混沌系统不同, 系统只有一个平衡点, 初始条件在系统能振荡的情况下不影响系统状态. 电路实验仿真结果和数值仿真具有很好的一致性, 证实了该系统的存在性和物理上可实现性.Based on a proposed voltage-controlled memristor, a simplest parallel memristor chaotic system is constructed. The dynamical characteristics of the new chaotic system are analyzed, including Lyapunov exponent, Lyapunov dimension, time domain waveforms, portrait diagrams, Lyapunov exponent spectrum, bifurcation diagrams and Poincar mapping. An electronic circuit of the new system is designed and verified by simulations using the EWB software. Research results show that with the parameter change, the i-v characteristic of the memristor, instead of keeping inclined 8-shaped, becomes a fan-shape with a tail. The differences between the chaotic system and the magnetic-controlled memristor chaotic system are in two aspects: only one equilibrium point in the chaotic system, and the initial conditions do not affect the state of the system when the system can oscillate. Good matching between numerical simulation and circuit experimental simulation proves the existence and physical realizability of the new chaotic system.
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Keywords:
- memristor /
- chaotic circuit /
- parallel /
- dynamical behaviour
[1] Chua L O 1971 IEEE Trans. Circ. Theory 18 507
[2] Chua L O, Kang S M 1976 Proc. IEEE 64 209
[3] Tour J M, He T 2008 Nature 453 42
[4] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
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[11] Itoh M, Chua L O 2008 Int. J. Bifurc. Chaos 18 3183
[12] Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 许建平 2010 59 3785]
[13] Ivo P 2010 IEEE Trans. Circ. Syst. Ⅱ 57 975
[14] Itoh M, Chua L O 2010 Int. J Bifur Chaos 20 1567
[15] Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Ser. E 41 1135 (in Chinese) [包伯成, 史国栋, 许建平, 刘中, 潘赛虎 2011 中国科学E辑 41 1135]
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[1] Chua L O 1971 IEEE Trans. Circ. Theory 18 507
[2] Chua L O, Kang S M 1976 Proc. IEEE 64 209
[3] Tour J M, He T 2008 Nature 453 42
[4] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[5] Li H, Liao Z M, Wu H C, Tian X X, Xu D S, Cross G L W, Duesberg G S, Shvets I V, Yu D P 20ll Nano Let. ll 4601
[6] Nagata T, Haemori M, Yamashita Y, Yoshikawa H, Iwashita Y, Kobayashi K, Chikyow T 20ll Appl. Phys. Lett. 99 22351
[7] Joglekar Y N, Wolf S J 2009 Eur. J. Phys. 30 661
[8] Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[9] Shin S, Kim K, Kang S 2011 IEEE Trans Nano. 10 266
[10] Muthuswamy B 2010 Int. J. Bifur. Chaos 20 1335
[11] Itoh M, Chua L O 2008 Int. J. Bifurc. Chaos 18 3183
[12] Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 许建平 2010 59 3785]
[13] Ivo P 2010 IEEE Trans. Circ. Syst. Ⅱ 57 975
[14] Itoh M, Chua L O 2010 Int. J Bifur Chaos 20 1567
[15] Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Ser. E 41 1135 (in Chinese) [包伯成, 史国栋, 许建平, 刘中, 潘赛虎 2011 中国科学E辑 41 1135]
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