Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

doi:10.1088/1674-1056/26/11/110502

Abstract A novel 5-dimensional (5D) memristive chaotic system is proposed, in which multi-scroll hidden attractors and multi-wing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincaré map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.

Keywords: multi-scroll hidden attractors multi-wing hidden attractors multiple lines equilibria no equilibrium

Received: 24 April 2017
Revised: 01 August 2017
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Jn	(High-dimensional chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 51177117 and 51307130).

Corresponding Authors: Xiaoyu Hu
E-mail: huxiaoyucool@163.com

Cite this article:

Xiaoyu Hu(胡晓宇), Chongxin Liu(刘崇新), Ling Liu(刘凌), Yapeng Yao(姚亚鹏), Guangchao Zheng(郑广超) Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system 2017 Chin. Phys. B 26 110502

[1]	Han F, Hu J, Yu X and Wang Y 2007 Applied Mathematics and Computation 185 931
[2]	Gámez-Guzmán L, Cruz-Hernández C, López-Gutiérrez R M and García-Guerrero E E 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2765
[3]	Ben Slimane N, Bouallegue K and Machhout M 2017 Nonlinear Dyn.
[4]	Orue A B, Alvarez G, Pastor G, Romera M, Montoya F and Li S 2010 Commun. Nonlinear Sci. Numer. Simul. 15 3471
[5]	Yu S, Lü J and Chen G 2007 Phys. Lett. A 364 244
[6]	Dadras S and Momeni H R 2009 Phys. Lett. A 373 3637
[7]	Bao B, Wang X and Xu J 2010 2010 International Works hop on Chaos-Fractals Theories and Applications(IWCFTA) 211
[8]	Xu F and Yu P 2010 Journal of Mathematical Analysis& Applications 362 252
[9]	Tahir F R, Ali R S, Pham V T, Buscarino A, Frasca M and Fortuna L 2016 Nonlinear Dyn. 85 2665
[10]	Tang W K S, Zhong G Q, Chen G and Man K F 2001 IEEE Transactions on Circuits& Systems I:Fundamental Theory& Applications 48 1369
[11]	Zhang C and Yu S 2010 Phys. Lett. A 374 3029
[12]	Yu S, Lu J, Chen G and Yu X 2011 IEEE Transactions on Circuits& Systems Ⅱ:Express Briefs 58 314
[13]	Li F and Yao C 2016 Nonlinear Dyn. 84 2305
[14]	Ma J, Wu X, Chu R and Zhang L 2014 Nonlinear Dyn. 76 1951
[15]	Yalçin M E 2007 Chaos Soliton. Fract. 34 1659
[16]	Bao B, Zhou G, Xu J and Liu Z 2010 Int. J. Bifurcation Chaos 20 2203
[17]	Ahmad W M 2005 Chaos Soliton. Fract. 25 727
[18]	Deng W and Lü J 2007 Phys. Lett. A 369 438
[19]	Cang S, Wu A, Wang Z, Xue W and Chen Z 2015 Nonlinear Dyn. 83 1987
[20]	Zhou L, Wang C and Zhou L 2016 Nonlinear Dyn. 85 2653
[21]	Wang C, Xia H and Zhou L 2017 Int. J. Bifurcation Chaos 27 1750091
[22]	Zhou L, Wang C and Zhou L 2017 Int. J. Bifurcation Chaos 27 1750027
[23]	Dudkowski D, Jafari S, Kapitaniak T, Kuznetsov N V, Leonov G A and Prasad A 2016 Physics Reports 637 1
[24]	Leonov G A and Kuznetsov N V 2013 Int. J. Bifurcation Chaos 23 1330002
[25]	Kuznetsov N V 2016 AETA 2015:Recent Advances in Electrical Engineering and Related Sciences 371 13
[26]	Wang X and Chen G 2012 Commun. Nonlinear Sci. Numer. Simul. 17 1264
[27]	Molaie M, Jafari S, Sprott J C and Golpayegani S M R H 2013 Int. J. Bifurcation Chaos 23 1350188
[28]	Wei Z 2011 Phys. Lett. A 376 102
[29]	Jafari S, Sprott J C and Hashemi Golpayegani S M R 2013 Phys. Lett. A 377 699
[30]	Jafari S and Sprott J C 2013 Chaos Soliton. Fract. 57 79
[31]	Tahir F R, Jafari S, Pham V T, Volos C and Wang X 2015 Int. J. Bifurcation Chaos 25 1550056
[32]	Zhou L, Wang C and Zhou L 2017 International Journal of Circuit Theory and Applications
[33]	Hu X, Liu C, Liu L, Ni J and Li S 2016 Nonlinear Dyn. 86 1725
[34]	Jafari S, Pham V T and Kapitaniak T 2016 Int. J. Bifurcation Chaos 26 1650031
[35]	Chua L 1971 IEEE Transactions on Circuit Theory 18 507
[36]	Li C and Sprott J C 2014 Int. J. Bifurcation Chaos 24 1450131
[37]	Li C and Sprott J C 2014 Int. J. Bifurcation Chaos 24 1450034
[38]	Sharma P R, Shrimali M D, Prasad A, Kuznetsov N V and Leonov G A 2015 The European Physical Journal Special Topics 224 1485

[1]	An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[2]	A color image encryption algorithm based on hyperchaotic map and DNA mutation Xinyu Gao(高昕瑜), Bo Sun(孙博), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). Chin. Phys. B, 2023, 32(3): 030501.
[3]	Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system Huamei Yang(杨华美) and Yuangen Yao(姚元根). Chin. Phys. B, 2023, 32(2): 020501.
[4]	Epilepsy dynamics of an astrocyte-neuron model with ammonia intoxication Zhixuan Yuan(袁治轩), Mengmeng Du(独盟盟), Yangyang Yu(于羊羊), and Ying Wu(吴莹). Chin. Phys. B, 2023, 32(2): 020502.
[5]	Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[6]	Resonance and antiresonance characteristics in linearly delayed Maryland model Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[7]	A novel hyperchaotic map with sine chaotification and discrete memristor Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). Chin. Phys. B, 2022, 31(12): 120501.
[8]	Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Chin. Phys. B, 2022, 31(10): 100504.
[9]	Periodic and chaotic oscillations in mutual-coupled mid-infrared quantum cascade lasers Zhi-Wei Jia(贾志伟), Li Li(李丽), Yi-Yan Guo(郭一岩), An-Bang Wang(王安帮), Hong Han(韩红), Jin-Chuan Zhang(张锦川), Pu Li(李璞), Shen-Qiang Zhai(翟慎强), and Feng-Qi Liu(刘峰奇). Chin. Phys. B, 2022, 31(10): 100505.
[10]	Exponential sine chaotification model for enhancing chaos and its hardware implementation Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Chin. Phys. B, 2022, 31(8): 080508.
[11]	Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises Gang Zhang(张刚), Yu-Jie Zeng(曾玉洁), and Zhong-Jun Jiang(蒋忠均). Chin. Phys. B, 2022, 31(8): 080502.
[12]	Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[13]	Effect of astrocyte on synchronization of thermosensitive neuron-astrocyte minimum system Yi-Xuan Shan(单仪萱), Hui-Lan Yang(杨惠兰), Hong-Bin Wang(王宏斌), Shuai Zhang(张帅), Ying Li(李颖), and Gui-Zhi Xu(徐桂芝). Chin. Phys. B, 2022, 31(8): 080507.
[14]	Research and application of stochastic resonance in quad-stable potential system Li-Fang He(贺利芳), Qiu-Ling Liu(刘秋玲), and Tian-Qi Zhang(张天骐). Chin. Phys. B, 2022, 31(7): 070503.
[15]	Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system Sheng-Hao Jia(贾生浩), Yu-Xia Li(李玉霞), Qing-Yu Shi(石擎宇), and Xia Huang(黄霞). Chin. Phys. B, 2022, 31(7): 070505.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

Cite this article:

Online attention