Indian Journal of Physics

, Volume 93, Issue 9, pp 1187–1194 | Cite as

Impulsive anti-synchronization control for fractional-order chaotic circuit with memristor

  • Fanqi MengEmail author
  • Xiaoqin Zeng
  • Zuolei Wang
Original Paper


This paper investigates the anti-synchronization of fractional-order memristive chaotic circuits (FMCC) with time delay via an impulsive control scheme. Based on the Mittag-Leffler function, the impulsive control principle and the Lyapunov stability theory, several criteria are adopted to derive the impulsive anti-synchronization of FMCC with time delay. Finally, numerical examples are exploited to verify the effectiveness of the theoretical analysis, and some discussions about the stable region are given.


Fractional order Memristor Chaos Anti-synchronization Impulsive control 





This work is supported by the National Science Foundation of China (Grants Nos. 51777180, 11771376).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


  1. [1]
    L O Chua IEEE Circuit Theory 18(5) 507 (1971)CrossRefGoogle Scholar
  2. [2]
    D B Strukov, G S Snider, D R Stewart and R S.Williams Nature 453 80 (2008)ADSCrossRefGoogle Scholar
  3. [3]
    J M Tour and T He Nature 453 42 (2008)Google Scholar
  4. [4]
    X L Shi, S K Duan, L D Wang, T W Huang and C D Li Neurocomputing 166(C) 487 (2015)Google Scholar
  5. [5]
    B Wang, F C Zou and J Cheng Optik 154 538 (2017)ADSCrossRefGoogle Scholar
  6. [6]
    Y B Zhao, X Z Zhang, J Xu and Y C Guo Chaos Solitons Fractals 81(A) 315 (2015)Google Scholar
  7. [7]
    R Hilfer (New Jersey: World Scientific) (2001)Google Scholar
  8. [8]
    K Moaddy, A G Radwan, K N Salama, S Momani and I Hashim Comput. Math. Appl. 64(10) 3329 (2012)MathSciNetCrossRefGoogle Scholar
  9. [9]
    D Tripathi, S K Pandey and S Das Appl. Math. Comput. 215(10) 3645 (2010)MathSciNetGoogle Scholar
  10. [10]
    A Kumar and S Kumar Proc Natl Acad. Sci. Sect. A Phys. Sci. 1–12 (2017)Google Scholar
  11. [11]
    G A Anastassiou, I K Argyros and S Kumar Fundam. Inform. 151 241 (2017)MathSciNetCrossRefGoogle Scholar
  12. [12]
    L X Yang and J Jiang Discrete Dyn. Nat. Soc. 3 485 (2013)Google Scholar
  13. [13]
    H L Li, C Hu, Y L Jiang, Z L Wang and Z D Teng Chaos Solitons Fractals 92 142 (2016)ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    X D Ding, J D Cao, X Zhao and F E Alsaadi Neural Process. Lett. 46 561 (2017)CrossRefGoogle Scholar
  15. [15]
    R Rakkiyappan, G Velmurugan and J D Cao Nonlinear Dyn. 78(4) 2823 (2014)CrossRefGoogle Scholar
  16. [16]
    J D Cao, R Sivasamy and R Rakkiyappan Circuits Syst. Signal Process. 35 811 (2016)CrossRefGoogle Scholar
  17. [17]
    J Ma, A H Zhang, Y F Xia and L P Zhang Appl. Math. Comput. 215(9) 3318 (2010)MathSciNetGoogle Scholar
  18. [18]
    X Y Wang, X L Gao and L L Wang. Int. J. Mod. Phys. A 27(09) 1350033 (2013)Google Scholar
  19. [19]
    R L Magin Crit. Rev. Biomed. Eng. 32 195 (2004)Google Scholar
  20. [20]
    J Ma, L Mi, P Zhou, Y Xu and T Hayat. Appl. Math. Comput. 307 321 (2017)MathSciNetGoogle Scholar
  21. [21]
    J Ma, F Q Wu and C N Wang Int. J. Mod. Phys. B 31(2) 1650251 (2016)Google Scholar
  22. [22]
    T Yang and L O Chua IEEE Circuits Syst. 44(10) 976 (1997)Google Scholar
  23. [23]
    J Garcíaojalvo and R Roy. Phys. Rev. Lett. 86(22) 5204 (2001)ADSCrossRefGoogle Scholar
  24. [24]
    W G Xia and J D Cao Chaos 19(1) 013120 (2009)Google Scholar
  25. [25]
    S K Agrawal, M Srivastava and S Das Chaos Solitons Fractals 45(6) 737 (2012)ADSCrossRefGoogle Scholar
  26. [26]
    H Q Wu, L F Wang, P F Niu and Y Wang Neurocomputing 235(C) 264 (2017)Google Scholar
  27. [27]
    W Xiong and J J Huang Adv. Differ. Equ. 101 (2016)Google Scholar
  28. [28]
    I Stamova and G Stamov. Commun. Nonlinear Sci. 19(3) 702 (2014)MathSciNetCrossRefGoogle Scholar
  29. [29]
    I Stamova Nonlinear Dyn. 77(4) 1251 (2014)MathSciNetCrossRefGoogle Scholar
  30. [30]
    Q J Zhang, J A Lu and J C Zhao Commun. Nonlinear Sci. 15(4) 1063 (2010)MathSciNetCrossRefGoogle Scholar
  31. [31]
    X Y Wang, Y L Zhang, D Lin and N Zhang Chin. Phys. B 20 030506 (2011)ADSCrossRefGoogle Scholar
  32. [32]
    W H Chen, Z Y Jiang, J C Zhong and X M Lu. J Frankl. I 351 4084 (2014)CrossRefGoogle Scholar
  33. [33]
    J Q Lu, Z D Wang, J D Cao, D W C Ho and J Kurths Int. J. Bifurc. Chaos 22(07) 1250176 (2012)CrossRefGoogle Scholar
  34. [34]
    H G Wu, S Y Chen and B C Bao Acta Phys. Sin. 64(3) 030501 (2015)Google Scholar
  35. [35]
    A Chandrasekar and R Rakkiyappan Neurocomputing 173 1348 (2016)Google Scholar
  36. [36]
    I Petras. IEEE Trans Circuits II 57(12) 975 (2010)Google Scholar
  37. [37]
    J G Liu Chin. Phys. B 22 060501 (2013)Google Scholar
  38. [38]
    W Ma, C Y Li, Y J Wu Chaos 26(8) 084311 (2016)ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    I Stamova Appl. Math. Comput. 237(3) 605 (2014)MathSciNetGoogle Scholar
  40. [40]
    I Stamova and G Stamov Functional and Impulsive Differential Equations of Fractional Order (2017)Google Scholar
  41. [41]
    F Wang, Y Q Yang, A H Hu and X Y Xu Nonlinear Dyn. 82(4) 1979 (2015)MathSciNetGoogle Scholar
  42. [42]
    I Podlubny Mathematics in Science and Engineering (1999).Google Scholar
  43. [43]
    N Aguila-Camacho, M A Duarte-Mermoud and J A Gallegos Commun. Nonlinear Sci. 19(9) 2951 (2014)MathSciNetCrossRefGoogle Scholar
  44. [44]
    M Saigo, R K Saxena and A A Kilbas. Integr. Transf. Spec. Funct. 15(1) 31 (2004)Google Scholar
  45. [45]
    S Liang, R C Wu and L P Chen. Physica A 444, 49–62 (2016)ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    F Wang and Y Q Yang Physica A 482, 158–172 (2017)ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    B C Bao, W Hu, J P Xu, Z Liu and L Zhou Acta Phys. Sin. 60(12) 1775 (2011)Google Scholar
  48. [48]
    K Diethelm, N J Ford and A D Freed Nonlinear Dyn. 29 3 (2002)Google Scholar

Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.Computer and Information Engineering CollegeHohai UniversityNanjingPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsYancheng Teachers UniversityYanchengPeople’s Republic of China

Personalised recommendations