Multistability and coexisting transient chaos in a simple memcapacitive system

doi:10.1088/1674-1056/ab7e98

Abstract The self-excited attractors and hidden attractors in a memcapacitive system which has three elements are studied in this paper. The critical parameter of stable and unstable states is calculated by identifying the eigenvalues of Jacobian matrix. Besides, complex dynamical behaviors are investigated in the system, such as coexisting attractors, hidden attractors, coexisting bifurcation modes, intermittent chaos, and multistability. From the theoretical analyses and numerical simulations, it is found that there are four different kinds of transient transition behaviors in the memcapacitive system. Finally, field programmable gate array (FPGA) is used to implement the proposed chaotic system.

Keywords: memcapacitive system multistability coexisting attractors transient transition behaviors

Received: 06 January 2020
Revised: 02 March 2020
Accepted manuscript online:

PACS:	85.25.Hv	(Superconducting logic elements and memory devices; microelectronic circuits)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 51377124) and the Science Fund for New Star of Youth Science and Technology of Shaanxi Province, China (Grant No. 2016KJXX-40).

Corresponding Authors: Fa-Qiang Wang
E-mail: faqwang@xjtu.edu.cn

Cite this article:

Fu-Ping Wang(王富平), Fa-Qiang Wang(王发强) Multistability and coexisting transient chaos in a simple memcapacitive system 2020 Chin. Phys. B 29 058502

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Rössler 1976 Phys. Lett. A. 57 397
[3]	Chen G and Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[4]	Lü J and Chen G 2002 Int. J. Bifur. Chaos 12 659
[5]	Chua L O and Lin G N 1990 IEEE Trans. Circuits Syst. 37 885
[6]	Liu C, Liu L, Liu T and Li P 2004 Chaos Solitons Fractals 22 1031
[7]	Kuznetsov N V, Leonov G A and Vagaitsev S 2010 IFAC Proc. 43 29
[8]	Dudkowski D, Jafari S, Kapitaniak T, Kuznetsov N V, Lwonov G A and Prasad A 2016 Phys. Rep. 637 1
[9]	Kuznetsov N and Leonov G 2014 IFAC Proc. 47 5445
[10]	Liu Y F, Yang D D, Wang L X and Li Q 2018 Chin. Phys. Lett. 35 046801
[11]	Jia M M, Jiang H G and Li W J 2019 Acta Phys. Sin. 68 130503 (in Chinese)
[12]	Zhou W, Wang G, Shen Y, Yuan F and Yu S 2018 Int. J. Bifur. Chaos 28 1830033
[13]	Pham V T, Jafari S, Kapitaniak T, Volos C and Kingni S T 2017 Int. J. Bifur. Chaos 27 1750053
[14]	Sprott J C, Wang X and Chen G 2013 Int. J. Bifur. Chaos 23 1350093
[15]	Barati K, Jafari S, Sprott J C and Pham V T 2016 Int. J. Bifur. Chaos 26 1630034
[16]	Lai Q, Akgul A, Zhao X W and Pei H 2017 Int. J. Bifur. Chaos 27 1750142
[17]	Pham V T, Volos C, Jafari S and Kapitaniak T 2017 Nonlinear Dyn. 87 2001
[18]	Wei Z, Moroz I, Sprott J C, Akgul A S and Zhang W 2017 Chaos 27 033101
[19]	Wang G, Shi C, Wang X and Yuan F 2017 Math. Probl. Eng. 2017 6504969
[20]	Yuan F, Wang G, Shen Y and Wang X 2016 Nonlinear Dyn. 86 37
[21]	Mou J, Sun K, Ruan J and He S 2016 Nonlinear Dyn. 86 1735
[22]	Lai Y C and Tél T 2011 Transient chaos: complex dynamics on finite time scales, Vol. 173 (New York: Springer) pp. 1-103
[23]	Croquette V and Poitou C 1981 J. Physique Lett. 42 1353
[24]	Arecchi F T, Meucci R, Puccioni G and Tredicce J 1982 Phys. Rev. Lett. 49 1217
[25]	Arecchi F T and Lisi F 1983 Phys. Rev. Lett. 50 1330
[26]	Sathiyadevi K, Karthiga S, Chandrasekar V K, Senthilkumar D V and Lakshmanan M 2019 Commun. Nonlinear Sci. Numer. Simul. 72 586
[27]	Maslennikov O V, Nekorkin V I and Jürgen K 2018 Chaos 28 033107
[28]	Danca M F 2016 Nonlinear Dyn. 86 1263
[29]	Bao B C, Jiang P, Wu H G and Hu F W 2015 Nonlinear Dyn. 79 2333
[30]	Bao H, Wang L, Bao B C and Wang G Y 2018 Commun. Nonlinear Sci. Numer. Simul. 57 264
[31]	Dong E Z, Yuan M F, Zhang C, Tong J G, Chen Z Q and Du S Z 2018 Int. J. Bifur. Chaos 28 1850081
[32]	Jia H, Guo Z, Wang S and Chen Z 2018 Int. J. Bifur. Chaos 28 1850161
[33]	Elkholy M M, Elkholy H M E and Elkouny A 2016 IEEE Procedding of 10th International Conference on Computer Engineering & Systems (ICCES), December 23-24, 2015, Cairo, EGYPT pp. 81-85
[34]	Mauricio Z D L H, Leonardo A and Yolanda V 2015 Sci. World J. 2015 1
[35]	Rajagopal K, Panahi S, Karthikeyan A, Alsaedi A, Pham V T and Hayat T 2018 Int. J. Bifur. Chaos 28 1850164
[36]	Dong E Z, Wang Z, Yu X, Chen Z Q and Wang Z H 2018 Chin. Phys. B 27 010503
[37]	Dong E Z, Liang Z H, Du S Z and Chen Z Q 2016 Nonlinear Dyn. 83 623
[38]	Di Ventra M, Pershin Y V and Chua L O 2009 Proc. IEEE 97 1717
[39]	Adhikari S P, Sah M P, Kim H and Chua L O 2013 IEEE Trans. Circuits Syst. I-Regul. Paper 60 3008
[40]	Leonov G A, Kuznetsov N V and Vagaitsev V I 2012 Physica D 241 1482
[41]	Leonov G A, Kuznetsov N V and Mokaev T 2015 Eur. Phys. J. Spec. Top. 224 1421
[42]	Leonov G A and Kuznetsov N V 2013 Int. J. Bifurc. Chaos 23 1330002
[43]	Dance M 2017 Nonlinear Dyn. 89 577
[44]	Rajagopal K, Guessas L, Vaidyanathan S, Karthikeyan A and Srinivasan A 2017 Math. Probl. Eng. 2017 7307452
[45]	Rajagopal K, Jafari S and Laarem G 2017 Pramana - J. Phys. 89 92
[46]	Li C, Sprott J C, Liu Y, Gu Z and Zhang J 2018 Int. J. Bifur. Chaos 28 1850163

[1]	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.
[2]	Continuous non-autonomous memristive Rulkov model with extreme multistability Quan Xu(徐权), Tong Liu(刘通), Cheng-Tao Feng(冯成涛), Han Bao(包涵), Hua-Gan Wu(武花干), and Bo-Cheng Bao(包伯成). Chin. Phys. B, 2021, 30(12): 128702.
[3]	Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷). Chin. Phys. B, 2021, 30(12): 120502.
[4]	Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation Zong-Li Yang(杨宗立), Dong Liang(梁栋), Da-Wei Ding(丁大为), Yong-Bing Hu(胡永兵), and Hao Li(李浩). Chin. Phys. B, 2021, 30(12): 120515.
[5]	A memristive map with coexisting chaos and hyperchaos Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强). Chin. Phys. B, 2021, 30(11): 110502.
[6]	Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors Li-Lian Huang(黄丽莲), Shuai Liu(刘帅), Jian-Hong Xiang(项建弘), and Lin-Yu Wang(王霖郁). Chin. Phys. B, 2021, 30(10): 100506.
[7]	A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Qin-Sheng Bi(毕勤胜). Chin. Phys. B, 2020, 29(6): 060501.
[8]	Dynamics of the two-SBT-memristor-based chaotic circuit Mei Guo(郭梅), Meng Zhang(张萌), Ming-Long Dou(窦明龙), Gang Dou(窦刚), and Yu-Xia Li(李玉霞). Chin. Phys. B, 2020, 29(11): 110505.
[9]	A new nonlinear oscillator with infinite number of coexisting hidden and self-excited attractors Yan-Xia Tang(唐妍霞), Abdul Jalil M Khalaf, Karthikeyan Rajagopal, Viet-Thanh Pham, Sajad Jafari, Ye Tian(田野). Chin. Phys. B, 2018, 27(4): 040502.
[10]	Parameter analysis of chaotic superlattice true random number source Yan-Fei Liu(刘延飞), Dong-Dong Yang(杨东东), Hao Zheng(郑浩), Li-Xin Wang(汪立新). Chin. Phys. B, 2017, 26(12): 120502.
[11]	Optical bistability and multistability via double dark resonance in graphene nanostructure Seyyed Hossein Asadpour, G Solookinejad, M Panahi, E Ahmadi Sangachin. Chin. Phys. B, 2016, 25(6): 064201.
[12]	Optical bistability and multistability in a defect slab doped by GaAs/AlGaAs multiple quantum wells Seyyed Hossein Asadpour, G Solookinejad, M Panahi, E Ahmadi Sangachin. Chin. Phys. B, 2016, 25(5): 054208.
[13]	Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns Gu Hua-Guang (古华光), Chen Sheng-Gen (陈胜根), Li Yu-Ye (李玉叶). Chin. Phys. B, 2015, 24(5): 050505.
[14]	Multistability of delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions Huang Yu-Jiao (黄玉娇), Hu Hai-Gen (胡海根). Chin. Phys. B, 2015, 24(12): 120701.
[15]	Optical bistability and multistability in a three-level Δ-type atomic system under the nonresonant condition Chen Ai-Xi(陈爱喜), Wang Zhi-Ping(王志平), Chen De-Hai(陈德海), and Xu Yan-Qiu(徐彦秋). Chin. Phys. B, 2009, 18(3): 1072-1076.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Multistability and coexisting transient chaos in a simple memcapacitive system

Cite this article:

Online attention