Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(12): 120515    DOI: 10.1088/1674-1056/ac1fdf
Special Issue: SPECIAL TOPIC— Interdisciplinary physics: Complex network dynamics and emerging technologies
SPECIAL TOPIC—Interdisciplinary physics: Complex network dynamics and emerging technologies Prev   Next  

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)1, Dong Liang(梁栋)1,2,†, Da-Wei Ding(丁大为)1,2,‡, Yong-Bing Hu(胡永兵)1, and Hao Li(李浩)3
1 School of Electronics and Information Engineering, Anhui University, Hefei 230601, China;
2 National Engineering Research Center for Agro-Ecological Big Data Analysis & Application, Anhui University, Hefei 230601, China;
3 State Grid Lu'an Electric Power Supply Company, Lu'an 237006, China
Abstract  This paper proposes a fractional-order simplest chaotic system using a bi-stable locally-active memristor. The characteristics of the memristor and transient transition behaviors of the proposed system are analyzed, and this circuit is implemented digitally using ARM-based MCU. Firstly, the mathematical model of the memristor is designed, which is nonvolatile, locally-active and bi-stable. Secondly, the asymptotical stability of the fractional-order memristive chaotic system is investigated and some sufficient conditions of the stability are obtained. Thirdly, complex dynamics of the novel system are analyzed using phase diagram, Lyapunov exponential spectrum, bifurcation diagram, basin of attractor, and coexisting bifurcation, coexisting attractors are observed. All of these results indicate that this simple system contains the abundant dynamic characteristics. Moreover, transient transition behaviors of the system are analyzed, and it is found that the behaviors of transient chaotic and transient period transition alternately occur. Finally, the hardware implementation of the fractional-order bi-stable locally-active memristive chaotic system using ARM-based STM32F750 is carried out to verify the numerical simulation results.
Keywords:  fractional calculus      bi-stable locally-active memristor      transient transition behaviors      ARM implementation  
Received:  23 June 2021      Revised:  29 July 2021      Accepted manuscript online:  22 August 2021
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  45.10.Hj (Perturbation and fractional calculus methods)  
  47.10.Fg (Dynamical systems methods)  
Corresponding Authors:  Dong Liang, Da-Wei Ding     E-mail:;

Cite this article: 

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) Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation 2021 Chin. Phys. B 30 120515

[1] Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2] Strukov D B, Snider G S, Stewart D R and Williams R S 2008 Nature 453 80
[3] Yao W, Wang C H, Cao J D, Sun Y C and Zhou C 2019 Neurocomputing 363 281
[4] Rajagopal K, Parastesh F, Azarnoush H, Hatef B, Jafari S and Berec V 2019 Chaos 29 043109
[5] Lin H R, Wang C H, Sun Y C and Yao W 2020 Nonlinear Dyn. 100 3367
[6] Han X, Sun B W, Xu R X, Xu J, Hong W and Qian K 2021 Chinese J. Inorg. Chem. 37 577
[7] Strukov D B 2016 Appl. Phys. A 122 302
[8] Pabst O, Martinsen R G and Chua L O 2019 Sci. Rep. 9 19260
[9] Zhou L, Wang C H and Zhou L L 2017 Int. J. Circ. Theor. Appl. 46 84
[10] Li C B, Thio W J C, Lu H H C and Lu T A 2018 IEEE Access 6 12945
[11] Muthuswamy B and Chua L O 2010 Int. J. Bifurcat. Chaos 20 1567
[12] Zhan K,Wei D, Shi J H and Yu J 2017 J. Electronic Imaging 26 013021
[13] Yu F, Zhang Z N, Liu L, Shen H, Huang Y Y, Shi C Q, Cai S, Du S C and Xu Q 2020 Complexity Special Issue 2020 5859273
[14] Chai X L, Gan Z H, Yuan K, Chen Y R and Liu X X 2019 Neural Comput. Applic. 31 219
[15] Xu K D, Li D H, Jiang Y N and Chen Q 2021 Front. Phys. 9 648737
[16] Huang Y C, Liu J X, Harkin J, McDaid L and Luo Y L 2021 Neurocomputing 423 336
[17] Liu Y, Guo Z, Chau T K, Lu H C and Si G Q 2021 Int. J. Circ. Theory Applic. 49 513
[18] Yu F, Qian S, Chen X, Huang Y Y, Liu L Shi C Q, Cai S, Song Y and Wang C H 2020 Int. J. Bifurcat. Chaos 30 2050147
[19] Korneev I A, Vadivasova T E and Semenov V V 2017 Nonlinear Dyn. 89 2829
[20] Amador A, Freire E, Ponce E and Ros J 2017 Int. J. Bifurcat. Chaos 27 17300221
[21] Zhu B M, Fan Q H, Li G Q and Wang D Q 2021 Analog Integr. Circ. Sig. Process 107 309
[22] Wang Z L, Min F H and Wang E R 2016 AIP Advances 6 095316
[23] Chen C J, Chen J Q, Bao H, Chen Mo and Bao B C 2019 Nonlinear Dyn. 95 3385
[24] Xie W L, Wang C H and Lin H R 2021 Nonlinear Dyn. 104 4523
[25] Zhu M H, Wang C H, Deng Q L and Hong Q H 2020 Int. J. Bifurcat. Chaos 30 2050184
[26] Gu M Y, Wang G Y, Liu J B, Liang Y, Dong Y J and Ying J J 2021 Int. J. Bifurcat. Chaos 31 2130018
[27] Ascoli A, Demirkol A S, Tetzlaff R, Slesazeck S, Mikolajick T and Chua L O 2021 Front. Neurosci. 15 651452
[28] LiZ J, Zhou H Y, Wang M J and Ma M L 2021 Nonlinear Dyn. 104 063154
[29] Zhu M H, Wang C H, Deng Q L and Hong Q H 2020 Int. J. Bifurcat. Chaos 30 2050184
[30] Klaus M and Chua L O 2013 Local Activity Principle (Imperial College Press) pp. 146-159
[31] Itoh M and Chua L O 2008 Int. J. Bifurcat. Chaos 18 3183
[32] Chua L O 2005 Int. J. Bifurcat. Chaos 15 3435
[33] Chua L O, Sirakoulis G C and Adamatzky A 2019 Handbook of Memristor Networks (Switzerland Cham:Springer Nature Switzerland AG) p. 89
[34] Mannan Z I, Choi H and Kim H 2016 Int. J. Bifurcat. Chaos 26 1630009
[35] Dong Y J, Wang G Y, Chen G R, Shen Y R and Ying J J 2020 Commun. Nonlinear Sci. Numer. Simul. 84 105203
[36] Jin P P, Wang G Y, Lu H H and Fernando T 2018 IEEE Transactions on Circuits and Systems II:Express Briefs 65 17524546
[37] Ying J J, Liang Y, Wang J L, Dong Y J, Wang G Y and Gu M Y 2021 Chaos, Solitons & Fractals 148 111038
[38] Ying J J, Liang Y, Wang G Y,Iu H H C,Zhang J and Jin P P 2021 Chaos 31 063114
[39] Ivo P, Chen Y Q and Calvin C 2009 IEEE Conference on Emerging Technologies & Factory Automation,September 22-25, 2009, Palma de Mallorca, Spain, p. 1
[40] Yu Y J and Wang Z H 2015 Acta Phys. Sin. 64 238401 (in Chinese)
[41] Fouda M E and Radwan A 2015 Circuits Syst. Signal Process. 34 961
[42] Yu Y J and Chen Y Q 15th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications August 18-21, 2019, Anaheim, California, USA, p. 7
[43] Wang S F and Ye A Q 2020 Symmetry Special Issue 12 437
[44] Tan Y M and Wang C H 2020 Chaos 30 053118
[45] Yu Y J, Bao H, Shi M, Bao B C, Chen Y Q and Chen M 2019 Complexity Special Issue 2019 2051053
[46] Ying J J, Wang G Y, Dong Y J and Yu S M 2019 Int. J. Bifurcat. Chaos 29 1930030
[47] Gibson G A, Musunuru S, Zhang J M, Vandenberghe K, Lee J, Hsieh C C, Jackson W, Jeon Y,Henze D, Li Z Y and Williams R S 2016 Appl. Phys. Lett. 108 023505
[48] Gorenflo R and Mainardi F 1997 Fractional calculus:integral and differential equations of fractional-order (New York:Springer Verlag) pp. 223-276
[49] Podlubny I 1999 Fractional Differential Equations (San Diego:Academic Press) p. 88
[50] Chua L O 1993 Communications and Computer Sci. E76-A 704
[51] Muthuswamy B and Chua L O 2010 Int. J. Bifurcat. Chaos 20 1567
[52] Ahmed E, El-Sayed A M A and El-Saka H A A 2007 J. Math. Anal. Appl. 325 542
[53] Adomian G 1990 Math. Comput. Model 13 17
[54] Bremen H F V, Udwadia F E and Proskurowski W 1997 Physica D 101 1
[55] Chithra A, Fonzin Fozin T, Srinivasan K, Mache Kengne E R, Tchagna Kouanou A and Raja Mohamed I 2021 Int. J. Bifurcat. Chaos 31 2150049
[56] Du C H, Liu L C, Zhang Z P and Yu S X 2021 Nonlinear Dyn. 104 765
[1] Modeling and character analyzing of multiple fractional-order memcapacitors in parallel connection
Xiang Xu(徐翔), Gangquan Si(司刚全), Zhang Guo(郭璋), and Babajide Oluwatosin Oresanya. Chin. Phys. B, 2022, 31(1): 018401.
[2] Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay
Mei Li(李梅), Ruo-Xun Zhang(张若洵), and Shi-Ping Yang(杨世平). Chin. Phys. B, 2021, 30(12): 120503.
[3] Multistability and coexisting transient chaos in a simple memcapacitive system
Fu-Ping Wang(王富平), Fa-Qiang Wang(王发强). Chin. Phys. B, 2020, 29(5): 058502.
[4] Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control
Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali. Chin. Phys. B, 2020, 29(5): 050504.
[5] Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order
Qiu-Yan He(何秋燕), Bo Yu(余波), Xiao Yuan(袁晓). Chin. Phys. B, 2017, 26(4): 040202.
[6] A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations
Li-Min Zhang(张立民), Ke-Hui Sun(孙克辉), Wen-Hao Liu(刘文浩), Shao-Bo He(贺少波). Chin. Phys. B, 2017, 26(10): 100504.
[7] Abundant solutions of Wick-type stochastic fractional 2D KdV equations
Hossam A. Ghany, Abd-Allah Hyder. Chin. Phys. B, 2014, 23(6): 060503.
[8] The fractional coupled KdV equations:Exact solutions and white noise functional approach
Hossam A. Ghany, A. S. Okb El Bab, A. M. Zabel, Abd-Allah Hyder. Chin. Phys. B, 2013, 22(8): 080501.
[9] Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative
Rajneesh Kumar, Vandana Gupta. Chin. Phys. B, 2013, 22(7): 074601.
[10] Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus
Wang Fa-Qiang, Ma Xi-Kui. Chin. Phys. B, 2013, 22(3): 030506.
[11] A new generalized fractional Dirac soliton hierarchy and its fractional Hamiltonian structure
Wei Han-Yu, Xia Tie-Cheng. Chin. Phys. B, 2012, 21(11): 110203.
[12] Exact solutions for nonlinear partial fractional differential equations
Khaled A. Gepreel, Saleh Omran. Chin. Phys. B, 2012, 21(11): 110204.
[13] Chaos in a fractional-order micro-electro-mechanical resonator and its suppression
Mohammad Pourmahmood Aghababa. Chin. Phys. B, 2012, 21(10): 100505.
[14] A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system
Si Gang-Quan, Sun Zhi-Yong, Zhang Yan-Bin. Chin. Phys. B, 2011, 20(8): 080505.
[15] Synchronization in a unified fractional-order chaotic system
Wu Zheng-Mao, Xie Jian-Ying. Chin. Phys. B, 2007, 16(7): 1901-1907.
No Suggested Reading articles found!