Dynamics analysis and circuit realization of Sprott-B
hyper-chaotic system based on memristor

doi:10.3969/j.issn.1007-5461.2021.03.016

Abstract

Abstract: A new fourth order hyperchaotic memristor system is constructed by introducing a magnetron memristor into the chaotic system. Firstly, the characteristics of the memristor system are discussed. The hyperchaotic characteristics of the new memristor system are determined by using analysis methods including Lyapunov exponent and dimension, dissipation, infinite multiple equilibrium sets and stability, and the infinite equilibrium sets are obtained. Compared with the original system, it is found that the new system is more complex and more chaotic. Secondly, the dynamic behavior of the new system is investigated, and the transient chaos caused by different parameters and the co-existence of attractors caused by different initial values are observed. This is the first analysis of this phenomenon for a system containing constant. Finally, the simulation electronic circuit of the system is designed andbuilt. The experimental results show that the oscilloscope results are consistent with the numerical simulation results, which provides a basis for the practical application of the memristor hyperchaotic system.

Key words: chaos, attractor coexisting, circuit implementation, memristor, transient chaos

CLC Number:

O415.5

LI Xiaoxia, ∗, WANG Xue, FENG Zhixin, ZHANG Qiyu, . Dynamics analysis and circuit realization of Sprott-B hyper-chaotic system based on memristor[J]. Chinese Journal of Quantum Electronics, 2021, 38(3): 393-404.

References 20

[1]	Chua L O. Memristor-The missing circuit element [J]. IEEE Transactions on Circuit Theory, 1971, 18(5): 507-519.
[2]	Wang L D, Drakakis E, Duan S K, et al. Memrietor model and its application for chaos generation [J]. International Journal
	of Bifurcation and Chaos, 2012, 22(8): 1250205.
[3]	Qiu L, Chen W, Wang F, et al. A non-local structural derivative model for memristor [J]. Chaos, Solitons and Fractals: The
	Interdisciplinary Journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, 2019, 126: 169-177.
[4]	Ou Q L, Xu L B, Guo Z Y, et al. Five order MCK chaotic circuit based on memristor [J]. Chinese Journal of Quantum
	Electronics, 2016, 33(1): 56-62.
	欧青立, 徐林波, 郭子叶, 等. 基于忆阻器的五阶MCK 混沌电路研究[J]. 量子电子学报, 2016, 33(1): 56-62.
[5]	Wu P, Li C, He X, et al. A memristor-based lorenz circuit and its stabilization via variable-time impulsive control [J]. International
	Journal of Bifurcation and Chaos, 2017, 27(3): 981-995.
[6]	Song X L, Wang C N, Li W C, et al. Synchronization of memristor circuits under time-varying coupling [J]. Chinese Journal
	of Quantum Electronics, 2015, 32(6): 719-727.
	宋欣林, 王春妮, 李文超, 等. 时变耦合下忆阻电路的同步[J]. 量子电子学报, 2015, 32(6): 719-727.
[7]	Zhang J, Liao X. Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse
[J]	AEU-International Journal of Electronics and Communications, 2017, 75: 82-90.
[8]	Wang C, He W, Tong Y, et al. Investigation and manipulation of different analog behaviors of memristor as electronic synapse
	for neuromorphic applications [J]. Scientific Reports, 2016, 6: 22970.
[9]	Yi L L, Ke J X. Research progress of chaotic secure optical communication [J]. Journal on Communications, 2020, 41(3):
16	8-181.
	义理林, 柯俊翔. 混沌保密光通信研究进展[J]. 通信学报, 2020, 41(3): 168-181.
[10]	Yan D W, Wang L D, Duan S K. Memristor-based multi-scroll chaotic system and its pulse synchronization control [J]. Acta
	Physica Sinica, 2018, 67(11): 50-63.
	闫登卫, 王丽丹, 段书凯. 基于忆阻器的多涡卷混沌系统及其脉冲同步控制[J]. 物理学报, 2018, 67(11): 50-63.
[11]	Wu H G, Bao B C, Liu Z. Scroll number and distribution control of attractor: System design and circuit realization [J]. Acta
	Physica Sinica, 2011, 60(9): 133-141.
	武花干, 包伯成, 刘中. 吸引子涡卷数量与分布的控制:系统设计及电路实现[J]. 物理学报, 2011, 60(9): 133-141.
[12]	Wang J L, Qin Z, Wu H N, et al. Analysis and pinning control for output synchronization and H∞ output synchronization of
	multiweighted complex networks [J]. IEEE Transactions on Cybernetics, 2018, 49(4): 1-13.
[13]	Lai Q, Xu G H, Pei H Q. Analysis and control of multiple attractors in Sprott B system [J]. Chaos, Solitons & Fractals, 2019,
12	3: 192-200.
[14]	Li X X, Li Y Y, Feng Z X, et al. Synchronization and parameter estimation of multiple-response chaotic systems with unknown
	parameters [J]. Chinese Journal of Quantum Electronics, 2019, 36(4): 483-489.
	李晓霞, 李艳雨, 冯志新, 等. 参数未知多响应混沌系统的同步及参数估计[J]. 量子电子学报, 2019, 36(4): 483-489.
[15]	Zhu H J, Zeng C B. Scaling and mixed synchronization foe different chaotic systems with totally unknown parameters [J].
	Control Theory & Applications, 2015, 32(3): 341-346.
	朱慧坚, 曾才斌. 参数完全未知的不同混沌系统的尺度与混合同步[J]. 控制理论与应用, 2015, 32(3): 341-346.
[16]	Sun J, Li X X, Zhang J H, et al. Synchronizability and eigenvalues of multilayer star networks through unidirectionally coupling
[J]	Acta Physica Sinica, 2017, 66(18): 188901.
	孙娟, 李晓霞, 张金浩, 等. 多层单向耦合星形网络的特征值谱及同步能力分析[J]. 物理学报, 2017, 66(18): 188901.
[17]	Zhang Y, Shu Y L. Analysis of a new high order Lorenz-type chaos model [J]. Mathematics in Practice and Theory, 2020,
50	(1): 216-222.
	张勇, 舒永录. 一类Lorenz 型高维混沌系统的分析[J]. 数学的实践与认识, 2020, 50(1): 216-222.
[18]	Bao B C, Liu Z. A hyperchaotic attractor coined from chaotic Lu system [J]. Chinese Physics Letters, 2008, 25(7): 2396-2399.
[19]	Li C B, Sprott J C, Thio W, et al. A new piecewise linear hyperchaotic circuit [J]. IEEE Transactions on Circuits and Systems
	II: Express Briefs, 2014, 61(12): 977-981.
[20]	Sun K, Sprott J C. Dynamics of a simplified Lorenz system [J]. International Journal of Bifurcation and Chaos, 2009, 19(4):
13	57-1366.
[21]	Gao Z Z. Chaos and controlling of unstable equilibrium point for a class of improved Sprott-J system [J]. Journal of Yancheng
	Institute of Technology (Natural Science Edition), 2011, 24(1): 17-20.
	高智中. 一类改进的Sprott-J 系统的混沌及其不稳定平衡点的控制[J]. 盐城工学院学报(自然科学版), 2011, 24(1):
17	-20.
[22]	Sprott J C. A new class of chaotic circuit [J]. Physics Letters A, 2000, 266(1): 19-23.
[23]	Liu Y Z, Fei S M. Chaos synchronization between the Sprott-B and Sprott-C with linear coupling [J]. Acta Physica Sinica,
20	06, 55(3): 1035-1039.
	刘扬正, 费树岷. Sprott-B 和Sprott-C 系统之间的耦合混沌同步[J]. 物理学报, 2006, 55(3): 1035-1039.
[24]	Fu J C, Sun J, Li P S. Analysis and control of a class of Sprott chaotic system with simple quadratic nonlinearities [J]. Journal
	of Jilin University (Science Edition), 2015, 53(3): 395-400.
	付景超, 孙敬, 李鹏松. 一类简单二次非线性Sprott 混沌系统的分析与控制[J]. 吉林大学学报(理学版), 2015, 53(3):
39	5-400.
[25]	Min G Q, Wang L D, Duan S K. Chaotic circuit of ion migration memristor and its application in the voice secure communication
[J]	Acta Physica Sinica, 2015, 64(21): 251-263.
	闵国旗, 王丽丹, 段书凯. 离子迁移忆阻混沌电路及其在语音保密通信中的应用[J]. 物理学报, 2015, 64(21): 251-263.
[26]	Xi H L, Li Y X, Huang X. Generation and nonlinear dynamical analyses of fractional-order memristor-based Lorenz systems
[J]	Entropy, 2014, 16(12): 6240-6253.
[27]	Ruan J Y, Sun K H, Mou J. Memristor-based Lorenz hyper-chaotic system and its circuit implementation [J]. Acta Physica
	Sinica, 2016, 65(19): 190502.
	阮静雅, 孙克辉, 牟俊. 基于忆阻器反馈的Lorenz 超混沌系统及其电路实现[J]. 物理学报, 2016, 65(19): 190502.
[28]	Wu H G, Chen S Y, Bao B C. Impulsive synchronization and initial value effect for a memristor-based chaotic system [J]. Acta
	Physica Sinica, 2015, 64(3): 209-216.
	武花干, 陈胜垚, 包伯成. 忆阻混沌系统的脉冲同步与初值影响研究[J]. 物理学报, 2015, 64(3): 209-216.
[29]	Wang W, Zeng Y C, Sun R T. Research on a six-order chaotic circuit with three memristors [J]. Acta Physica Sinica, 2017,
66	(4): 29-39.
	王伟, 曾以成, 孙睿婷. 含三个忆阻器的六阶混沌电路研究[J]. 物理学报, 2017, 66(4): 29-39.
[30]	Bao B C, Xu J P, Zhou G H, et al. Chaotic memristive circuit: Equivalent circuit realization and dynamical analysis [J]. Chinese
	Physics B, 2011, 20(12): 109-115.
[31]	Li J, Ye X D. Recent development of chaos theory in topological dynamics [J]. Acta Mathematica Sinica (English Series),
20	16, 32(1): 83-114.

Dynamics analysis and circuit realization of Sprott-B hyper-chaotic system based on memristor

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References 20

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	LI Xiaoxia, ∗, WANG Xue, FENG Zhixin, ZHANG Qiyu, XU Guizhi, . Research on a simple parallel chaotic system of memory elements [J]. Chinese Journal of Quantum Electronics, 2021, 38(4): 517-528.
[2]	LI Xiaoxia , ∗, FENG Zhixin , ZHANG Qiyu , WANG Xue , . Memristive multi-scroll chaotic system and its synchronization under sliding mode control [J]. Chinese Journal of Quantum Electronics, 2020, 37(6): 727-736.
[3]	ZHONG Dong-zhou*, XIAO Zhen-zhen, YANG Guang-ze. Criterion of globally complete chaos synchronization for diverse three-node VCSEL networks with coupling delays [J]. Chinese Journal of Quantum Electronics, 2019, 36(5): 575-583.
[4]	LI Xiaoxia1，2, LI Yanyu1，2, FENG Zhixin1，2, ZHANG Qiyu1，2. Synchronization and parameter estimation of multiple-response chaotic systems with unknown parameters [J]. Chinese Journal of Quantum Electronics, 2019, 36(4): 483-489.
[5]	. Image real-value encryption based on Logistic chaos [J]. J4, 2018, 35(2): 149-155.
[6]	He Ying，Zhang Haili，Shi Huangxia，Lu Jian. Improved Quantum Genetic Algorithm for identification of hyper-chaotic systems [J]. J4, 2016, 33(5): 578-583.
[7]	OU Qingli，XU Linbo，GUO Ziye, LI ya. Five order MCK chaotic circuit based on Memristor [J]. J4, 2016, 33(1): 56-62.
[8]	WAN Kang, XIE Shao-bin, ZHOU Shuang . Performance of chaotic spreading-spectrum sequences on phase-space repeatedly reconstructed mapping [J]. J4, 2015, 32(6): 713-718.
[9]	SONG Xinlin, Wang Chunn, LI Wenchao, MA Jun. Synchronization of Memristor Circuits under Time-varying Coupling [J]. J4, 2015, 32(6): 719-727.
[10]	HE Yujun， CHU Run-tong，LI Fan. Linear coupling-induced synchronization between periodic Chua oscillators [J]. J4, 2013, 30(5): 601-607.
[11]	LIU Peiyang, ZHAO Qingchun, YIN Hongxi . Performance analysis of two types of chaotic optical secure communication schemes [J]. J4, 2012, 29(4): 500-506.
[12]	KANG Wei-hong, CAOZheng-wen, LUO Rui, JIANG En-chun, ZHAO Long. A quantum identity authentication based on chaos [J]. J4, 2012, 29(2): 178-184.
[13]	XU Bi-rong. A digital secure communication scheme based on generalized synchronization of non-autonomous chaotic system [J]. J4, 2011, 28(6): 710-714.
[14]	CHU Run-Tong, WANG Chun-Ni, MA Jun. Synchronization and estimation of jump parameter of one certain chaotic circuit [J]. J4, 2010, 27(1): 82-87.
[15]	ZHOU Wu-Jie, YU Si-Min, XU Wei. Study and hardware implementation of n×m-scroll chaotic attractors [J]. J4, 2009, 26(6): 715-721.