Fractional-order simplest memristor-based chaotic circuit with new derivative

  • Jingya Ruan
  • Kehui Sun
  • Jun Mou
  • Shaobo He
  • Limin Zhang
Regular Article

Abstract.

In this paper, the fractional-order simplest memristor-based chaotic circuit is investigated based on the novel conformable Adomian decomposition method (CADM). Dynamics of this circuit is analyzed by employing bifurcation diagram, Lyapunov exponent spectrum, Poincaré section and other methods. The result shows that it has rich dynamical behaviors and we found the minimum order of this system for generating chaos is 1.08. To implement the system in digital circuit, the CADM iteration results with different items are compared to balance the speed and accuracy, and the suitable items are chosen for further application. Finally, DSP implementation of the system verifies the effectiveness of the solution algorithm.

References

  1. 1.
    S. Wang, B. Yan, Nonlinear Dyn. 73, 611 (2013)CrossRefGoogle Scholar
  2. 2.
    S. Das, Observation of Fractional Calculus in Physical System Description (Springer, Berlin, Heidelberg, 2011) pp. 101--156Google Scholar
  3. 3.
    V.E. Tarasov, Int. J. Mod. Phys. B 27, 1 (2015)Google Scholar
  4. 4.
    L. Liu, D. Liang, C. Liu, Nonlinear Dyn. 69, 1929 (2012)CrossRefGoogle Scholar
  5. 5.
    L. Godinho, J. Weberszpil, A. Helayel-Neto, Chaos, Solitons Fractals 45, 765 (2012)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    A. Carpinteri, F.M. Ed, Fractals and Fractional Calculus in Continuum Mechanics (Springer-Verlag, Vienna, 1997)Google Scholar
  7. 7.
    R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, J. Comput. Appl. Math. 264, 65 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    T. Abdeljawad, J. Comput. Appl. Math. 279, 57 (2014)CrossRefGoogle Scholar
  9. 9.
    S. He, K. Sun, X. Mei, B. Yan, S. Xu, Eur. Phys. J. Plus 132, 36 (2017)CrossRefGoogle Scholar
  10. 10.
    O.S. Iyiola, O. Tasbozan, A.K. Çesiz, Chaos, Solitons Fractals 97, 1 (2016)Google Scholar
  11. 11.
    W.S. Chung, J. Comput. Appl. Math. 290, 150 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Charef, H.H. Sun, Y.Y. Tsao, B. Onaral, IEEE Trans. Autom. Control 37, 1465 (1992)CrossRefGoogle Scholar
  13. 13.
    H.H. Sun, A.A. Abdelwahab, B. Onaral, IEEE Trans. Autom. Control 29, 441 (1984)CrossRefGoogle Scholar
  14. 14.
    G. Adomian, Comput. Math. Appl. 22, 101 (1991)MathSciNetCrossRefGoogle Scholar
  15. 15.
    S. He, K. Sun, H. Wang, Acta Phys. Sin. 63, 030502 (2014)Google Scholar
  16. 16.
    L.O. Chua, IEEE Trans. Circ. Theory 18, 507 (1971)CrossRefGoogle Scholar
  17. 17.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    B. Bao, Z. Ma, J. Xu, Z. Liu, Q. Xu, Int. J. Bifurc. Chaos 21, 2629 (2011)CrossRefGoogle Scholar
  19. 19.
    J. Sun, Y. Shen, Q. Yin, C. Xu, Chaos 23, 013140 (2013)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    J. Ruan, K. Sun, J. Mou, Acta Phys. Sin. 65, 190502 (2016)Google Scholar
  21. 21.
    F. Yuan, G. Wang, X. Wang, Chaos 26, 073107 (2016)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    B. Muthswamy, L.O. Chua, Int. J. Bifurc. Chaos 20, 1567 (2010)CrossRefGoogle Scholar
  23. 23.
    D. Cafagna, G. Grassi, Nonlinear Dyn. 70, 1185 (2012)CrossRefGoogle Scholar
  24. 24.
    K. Sun, X. Liu, C. Zhu, Chin. Phys. B 19, 110510 (2010)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jingya Ruan
    • 1
  • Kehui Sun
    • 1
  • Jun Mou
    • 1
  • Shaobo He
    • 2
  • Limin Zhang
    • 1
  1. 1.School of Physics and ElectronicsCentral South University ChangshaChangshaChina
  2. 2.School of Computer Science and TechnologyHunan University of Arts and ScienceChangdeChina

Personalised recommendations