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The European Physical Journal Special Topics

, Volume 228, Issue 10, pp 2133–2145 | Cite as

Parameter estimation in a new chaotic memristive system using ions motion optimization

  • Guiqin Kong
  • Yongxiang ZhangEmail author
  • Abdul Jalil M. Khalaf
  • Shirin Panahi
  • Iqtadar Hussain
Regular Article
Part of the following topical collections:
  1. Memristor-based Systems: Nonlinearity, Dynamics and Applications

Abstract

In this paper, a new four-dimensional nonlinear oscillator is introduced. This oscillator is memristive and can exhibit chaotic behavior. A complete dynamical analysis is done on each parameter of this system by the help of bifurcation diagram and Lyapunov exponents’ diagram. In order to estimate parameters of the proposed system, we use a new cost function based on the similarity between return maps. Then, with the help of ions motion optimization method, we minimize the obtained cost function and find the exact value of parameters.

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References

  1. 1.
    S. Jafari, J.C. Sprott, Chaos Solitons Fractals 57, 79 (2013)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Phys. Lett. A 377, 699 (2013)ADSMathSciNetGoogle Scholar
  3. 3.
    M. Molaie, S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Int. J. Bifurc. Chaos 23, 1350188 (2013)CrossRefGoogle Scholar
  4. 4.
    S. Ren, S. Panahi, K. Rajagopal, A. Akgul, V.T. Pham, S. Jafari, Z. Naturforsch. A 73, 239 (2018)ADSCrossRefGoogle Scholar
  5. 5.
    J. Singh, V.T. Pham, T. Hayat, S. Jafari, F.E. Alsaadi, B.K. Roy, Chin. Phys. B 27, 100501 (2018)ADSCrossRefGoogle Scholar
  6. 6.
    J.P. Singh, B.K. Roy, S. Jafari, Chaos Solitons Fractals 106, 243 (2018)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    J.C. Sprott, S. Jafari, V.T. Pham, Z.S. Hosseini, Phys. Lett. A 379, 2030 (2015)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    S. Jafari, V.-T. Pham, T. Kapitaniak, Int. J. Bifurc. Chaos 26, 1650031 (2016)CrossRefGoogle Scholar
  9. 9.
    Z. Liu, F. Wu, F. Alzahrani, J. Ma, Mod. Phys. Lett. B 32, 1850399 (2018)ADSCrossRefGoogle Scholar
  10. 10.
    C. Li, J.C. Sprott, Int. J. Bifurc. Chaos 24, 1450131 (2014)CrossRefGoogle Scholar
  11. 11.
    C. Li, J.C. Sprott, W. Hu, Y. Xu, Int. J. Bifurc. Chaos 27, 1750160 (2017)CrossRefGoogle Scholar
  12. 12.
    C. Li, J.C. Sprott, Y. Mei, Nonlinear Dyn. 89, 2629 (2017)CrossRefGoogle Scholar
  13. 13.
    C. Li, J.C. Sprott, Phys. Lett. A 382, 581 (2018)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    C. Li, W.J.C. Thio, J.C. Sprott, H.H.C. Iu, Y. Xu, IEEE Access 6, 29003 (2018)CrossRefGoogle Scholar
  15. 15.
    C. Hens, R. Banerjee, U. Feudel, S.K. Dana, Phys. Rev. E 85, 035202 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    H. Bao, N. Wang, B. Bao, M. Chen, P. Jin, G. Wang, Commun. Nonlinear Sci. Numer. Simul. 57, 264 (2018)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    M. Chen, M. Sun, B. Bao, H. Wu, Q. Xu, J. Wang, Nonlinear Dyn. 91, 1395 (2018)CrossRefGoogle Scholar
  18. 18.
    J.C. Sprott, S. Jafari, A.J.M. Khalaf, T. Kapitaniak, Eur. Phys. J. Special Topics 226, 1979 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    S. He, C. Li, K. Sun, S. Jafari, Entropy 20, 556 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    Z. Wei, V.T. Pham, A.J.M. Khalaf, J. Kengne, S. Jafari, Int. J. Bifurc. Chaos 28, 1850085 (2018)CrossRefGoogle Scholar
  21. 21.
    Y.-X. Tang, A.J.M. Khalaf, K. Rajagopal, V.T. Pham, S. Jafari, Y. Tian, Chin. Phys. B 27, 40502 (2018)CrossRefGoogle Scholar
  22. 22.
    N. Kuznetsov, G.A. Leonov, T.N. Mokaev, A. Prasad, M.D. Shrimali, Nonlinear Dyn. 92, 267 (2018)CrossRefGoogle Scholar
  23. 23.
    N. Kuznetsov, G.A. Leonov, T.N. Mokaev, S.M. Seledzhi, Hidden attractor in the Rabinovich system, Chua circuits and PLL, in AIP Conference Proceedings (AIP Publishing, 2016), Vol. 1738, p. 210008Google Scholar
  24. 24.
    N. Kuznetsov, G.A. Leonov, M.V. Yuldashev, R.V. Yuldashev, Commun. Nonlinear Sci. Numer. Simul. 51, 39 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    D. Dudkowski, S. Jafari, T. Kapitaniak, N.V. Kuznetsov, G.A. Leonov, A. Prasad, Phys. Rep. 637, 1 (2016)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    C. Li, J.C. Sprott, H. Xing, Nonlinear Dyn. 87, 1351 (2017)CrossRefGoogle Scholar
  27. 27.
    L.O. Chua, C.W. Wu, A. Huang, G.-Q. Zhong, IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 40, 732 (1993)CrossRefGoogle Scholar
  28. 28.
    K. Rajagopal, V.T. Pham, F.R. Tahir, A. Akgul, H.R. Abdolmohammadi, S. Jafari, Pramana 90, 52 (2018)ADSCrossRefGoogle Scholar
  29. 29.
    C. Volos, A. Akgul, V.T. Pham, I. Stouboulos, I. Kyprianidis, Nonlinear Dyn. 89, 1 (2017)CrossRefGoogle Scholar
  30. 30.
    F. Li, C. Yao, Nonlinear Dyn. 84, 1 (2016)CrossRefGoogle Scholar
  31. 31.
    C. Li, J.C. Sprott, W. Thio, H. Zhu, IEEE Trans. Circuits Syst. II: Express Briefs 61, 977 (2014)CrossRefGoogle Scholar
  32. 32.
    L. Chua, IEEE Trans. Circuit Theory 18, 507 (1971)CrossRefGoogle Scholar
  33. 33.
    L.O. Chua, S.M. Kang, Proc. IEEE 64, 209 (1976)MathSciNetCrossRefGoogle Scholar
  34. 34.
    J. Ruan, K. Sun, J. Mou, S. He, L. Zhang, Eur. Phys. J. Plus 133, 3 (2018)CrossRefGoogle Scholar
  35. 35.
    J. Ma, P. Zhou, B. Ahmad, G. Ren, C. Wang, PloS one 13, e0191120 (2018)CrossRefGoogle Scholar
  36. 36.
    V.-T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, N.V. Kuznetsov, T.M. Hoang, Eur. Phys. J. Special Topics 225, 127 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    V.-T. Pham, S. Jafari, S. Vaidyanathan, C. Volos, X. Wang, Sci. China Technol. Sci. 59, 358 (2016)CrossRefGoogle Scholar
  38. 38.
    R. Jing-Ya, S. Ke-Hui, M. Jun, Acta Phys. Sin. 65, 190502 (2016)Google Scholar
  39. 39.
    L. Xiang-Tao, Y. Ming-Hao, Chin. Phys. B 21, 050507 (2012)CrossRefGoogle Scholar
  40. 40.
    S. Jafari, S.M.R.H. Golpayegani, A. Daliri, Int. J. Comput. Math. 90, 903 (2013)MathSciNetCrossRefGoogle Scholar
  41. 41.
    S. Jafari, S.M.R.H. Golpayegani, M. Rasoulzadeh Darabad, Commun. Nonlinear Sci. Numer. Simul. 18, 811 (2013)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    S. Jafari, J.C. Sprott, V.T. Pham, S.M.R.H. Golpayegani, A.H. Jafari, Int. J. Bifurc. Chaos 24, 1450134 (2014)CrossRefGoogle Scholar
  43. 43.
    S.-K. Lao, Y. Shekofteh, S. Jafari, J.C. Sprott, Int. J. Bifurc. Chaos 24, 1450010 (2014)CrossRefGoogle Scholar
  44. 44.
    Y. Shekofteh, S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, F. Almasganj, Commun. Nonlinear Sci. Numer. Simul. 20, 469 (2015)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Y. Shekofteh, S. Jafari, K. Rajagopal, Soft Comput. 1 (2018)Google Scholar
  46. 46.
    Z. Wang, C. Volos, S.T. Kingni, A.T. Azar, V.T. Pham, Optik 131, 1071 (2017)ADSCrossRefGoogle Scholar
  47. 47.
    A. Stefanski, A. Dabrowski, T. Kapitaniak, Chaos Solitons Fractals 23, 1651 (2005)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    G.A. Leonov, N.V. Kuznetsov, Int. J. Bifurc. Chaos 17, 1079 (2007)CrossRefGoogle Scholar
  49. 49.
    N. Kuznetsov, T. Mokaev, P. Vasilyev, Commun. Nonlinear Sci. Numer. Simul. 19, 1027 (2014)ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    N. Kuznetsov, Phys. Lett. A 380, 2142 (2016)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    B. Chen, Y. Zhu, J. Hu, J.C. Principe, System parameter identification: Information criteria and algorithms (Newnes, 2013)Google Scholar
  52. 52.
    G.N. Vanderplaats, Numerical optimization techniques for engineering design (Vanderplaats Research and Development, Incorporated, 2001)Google Scholar
  53. 53.
    S. Jafari, J.C. Sprott, V.T. Pham, S.M.R.H. Golpayegani, A.H. Jafari, Int. J. Bifurc. Chaos 24, 1450134 (2014)CrossRefGoogle Scholar
  54. 54.
    B. Javidy, A. Hatamlou, S. Mirjalili, Appl. Soft Comput. 32, 72 (2015)CrossRefGoogle Scholar
  55. 55.
    M.S. Silberberg, Principles of general chemistry (McGraw-Hill Higher Education, New York, 2007)Google Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Guiqin Kong
    • 1
  • Yongxiang Zhang
    • 2
    Email author
  • Abdul Jalil M. Khalaf
    • 3
  • Shirin Panahi
    • 4
  • Iqtadar Hussain
    • 5
  1. 1.University of Jinan Library, University of JinanJinan, ShandongP.R. China
  2. 2.School of Mathematical Sciences, University of JinanJinan, ShandongP.R. China
  3. 3.Ministry of Higher Education and Scientific ResearchBaghdadIraq
  4. 4.Biomedical Engineering Department, Amirkabir University of TechnologyTehranIran
  5. 5.Department of MathematicsStatistics and Physics, Qatar UniversityDohaQatar

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