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Dynamics analysis of a fractional-order delayed SBT memristive chaotic system without equilibrium points

  • Dawei Ding
  • HuiLiu
  • Yecui Weng
  • Nian WangEmail author
Regular Article
  • 3 Downloads

Abstract.

The SBT memristor is a physical memristor using a Sr0.95Ba0.05TiO3 nanometer film, which is presented with a flux-controlled mathematical model. The integer-order chaotic systems based on SBT memristor have attracted much attention and have been thoroughly discussed. Analysis shows that the fractional-order system is closer to real system. In this paper, a fractional-order delayed SBT memristive chaotic system is proposed. It is worth noting that this fractional-order delayed SBT memristive system can produce chaotic attractors although it has no equilibrium points. A key system parameter is investigated by theoretical analyses and numerical simulations using the modified Adams-Bashforth-Moulton method. The results indicate that the system parameter can significantly affect the dynamic behavior, which can be indicated by the bifurcation diagrams, the Max Lyapunov exponent (MLE) diagram, the time domain waveform, the phase portraits and the power spectrum of the oscillator. All research can lay a significant theoretical foundation for the physical realization of chaotic circuits.

Notes

References

  1. 1.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    G. Ren, P. Zhou, J. Ma et al., Int. J. Bifurc. Chaos 27, 1750187 (2017)CrossRefGoogle Scholar
  3. 3.
    G. Ren, Y. Xu, C. Wang, Nonlinear Dyn. 88, 893 (2017)CrossRefGoogle Scholar
  4. 4.
    G. Zhang, J. Ma, A. Alsaedi et al., Appl. Math. Comput. 321, 290 (2018)MathSciNetGoogle Scholar
  5. 5.
    Y. Xu, Y. Jia, J. Ma et al., Chaos Solitons Fractals 104, 435 (2017)ADSCrossRefGoogle Scholar
  6. 6.
    F. Wu, C. Wang, W. Jin, J. Ma, Physica A 469, 81 (2017)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    S. Wen, Z. Zeng, T. Huang et al., IEEE Trans. Fuzzy Syst. 22, 1704 (2014)CrossRefGoogle Scholar
  8. 8.
    T. Driscoll, H.T. Kim, B.G. Chae et al., Appl. Phys. Lett. 95, 043503 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    T. Hasegawa, T. Ohno, K. Terabe et al., Adv. Mater. 22, 1831 (2010)CrossRefGoogle Scholar
  10. 10.
    T. Chang, S.H. Jo, K.H. Kim et al., Appl. Phys. A Mater. 102, 857 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Z.Q. Wang, H.Y. Xu, X.H. Li, H. Yu, Y.C. Liu, X.J. Zhu, Adv. Funct. Mater. 22, 2759 (2012)CrossRefGoogle Scholar
  12. 12.
    Y. Li, Y. Zhong, L. Xu, J. Zhang, X. Xu, H. Sun, X. Miao, Sci. Rep. 3, 1619 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    Y.X. Li, G. Dou, Int. J. Bifurc. Chaos 23, 1350204 (2013)CrossRefGoogle Scholar
  14. 14.
    Z. Wang, S. Joshi, S.E. Savelev et al., Nat. Mater. 16, 101 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    G. Dou, Y. Yu, M. Guo et al., Chin. Phys. Lett. 34, 038502 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    Y.M. Zhang, G. Dou, Z. Sun, M. Guo, Y.X. Li, Int. J. Bifurc. Chaos 27, 1750148 (2017)CrossRefGoogle Scholar
  17. 17.
    M. Guo, Z. Gao, Yb. Xue, G. Dou, Y.X. Li, Nonlinear Dyn 93, 1681 (2018)CrossRefGoogle Scholar
  18. 18.
    K.B. Oldham, Spanier, J. Math. Gaz. 56, 396 (1974)Google Scholar
  19. 19.
    Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Taza Gul, Discr. Contin. Dyn. Syst. S 13 (2020)Google Scholar
  20. 20.
    M.A. Khan, S. Ullah, M. Farooq, Chaos Solitons Fractals 116, 227 (2018)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Muhammad Altaf Khan, Saif Ullah, Muhammad Farhan, Discr. Contin. Dyn. Syst. S 13 (2020)Google Scholar
  22. 22.
    Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Eur. Phys. J. Plus 133, 237 (2018)CrossRefGoogle Scholar
  23. 23.
    Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Eur. Phys. J. Plus 133, 313 (2018)CrossRefGoogle Scholar
  24. 24.
    Muhammad Altaf Khan, Saif Ullah, Muhammad Farhan, AIMS Math. 4, 134 (2019)CrossRefGoogle Scholar
  25. 25.
    L. Chen, W. Pan, R. Wu, Y. He, ASME J. Comput. Nonlinear Dyn. 10, 064504 (2015)CrossRefGoogle Scholar
  26. 26.
    G. Velmurugan, R. Rakkiyappan, ASME J. Comput. Nonlinear Dyn. 11, 031016 (2016)CrossRefGoogle Scholar
  27. 27.
    A. Babakhani, D. Baleanu, R. Khanbabaie, Nonlinear Dyn. 69, 721 (2002)CrossRefGoogle Scholar
  28. 28.
    M. Xiao, W.X. Zheng, J. Cao, IEEE Trans. Neural Netw. Learn. Syst. 24, 118 (2013)CrossRefGoogle Scholar
  29. 29.
    A.Y.T. Leung, H.X. Yang, P. Zhu, Commun. Nonlinear Sci. Numer. Simul. 19, 1142 (2014)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    C. Huang, J. Cao, Z. Ma, Int. J. Syst. Sci. 47, 1 (2015)Google Scholar
  31. 31.
    W. Hu, D. Dawei, W. Nian, J. Comput. Nonlinear Dyn. 12, 041003 (2017)CrossRefGoogle Scholar
  32. 32.
    Dawei Ding, Xin Qian, Wei Hu, Nian Wang, Dong Liang, Eur. Phys. J. Plus 132, 11 (2017)CrossRefGoogle Scholar
  33. 33.
    V.-T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, N.V. Kuznetsov, T.M. Hoang, Eur. Phys. J. ST 225, 127 (2016)CrossRefGoogle Scholar
  34. 34.
    S. Bhalekar, V. Daftardar-Gejji, J. Fract. Calc. Appl. 1, 1 (2011)Google Scholar
  35. 35.
    M.D. Prokhorov, V.I. Ponomarenko, Chaos Solitons Fractals 63, 871 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Tang, Z. Wang, J.A. Fang, Commun. Nonlinear Sci. Numer. Simul. 15, 2456 (2010)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    V. Ponomarenko, M. Prokhorov, A. Karavaev, D. Kulminskiy, Nonlinear Dyn. 74, 1013 (2013)CrossRefGoogle Scholar
  38. 38.
    T.M. Hoang, M. Nakagawa, Chaos Solitons Fractals 38, 1423 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    S. Wang, Y. Yu, G. Wen, Nonlinear Anal. Hybrid Syst. 11, 129 (2014)MathSciNetCrossRefGoogle Scholar
  40. 40.
    A. Buscarino, L. Fortuna, M. Frasca, G. Sciuto, IEEE Trans. Circ. Syst. I 58, 1888 (2011)Google Scholar
  41. 41.
    A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Intelligent Computing and Signal Processing, Ministry of EducationAnhui UniversityHefeiChina
  2. 2.School of Electronics and Information EngineeringAnhui UniversityHefeiChina

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