Skip to main content
SpringerLink
Log in

Tracking multistability in the parameter space of a Chua’s circuit model

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The effect of applying an asymmetric periodic continuous-feedback signal F(x), which is a function of voltage x, across one of the capacitors in the classical Chua’s circuit model is examined. We have performed a numerical investigation on the dynamics of the Chua’s circuit model to discuss a procedure of distorting, suppressing and moving attractors and stable periodic structures (SPSs) in phase and parameter spaces, respectively, by accordingly choosing the control parameters in the function F(x). Increasing the asymmetry strength in F(x), we are able to track and to move overlapped SPSs related to multistability phenomenon in phase space, and to suppress SPSs related to one single attractor. Our results indicate that the methodology used here will have a wide spectrum of applications in generic nonlinear complex dynamical systems presenting multistability, related to both theoretical and experimental issues.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Fortuna, M. Frasca, M.G. Xibilia, Chua’s Circuit Implementations: Yesterday, Today and Tomorrow, World Scientific Series on Nonlinear Science. Series A (World Scientific Publisher, 2009)

  2. N.V. Stankevich, N.V. Kuznetsov, G.A. Leonov, L.O. Chua, Int. J. Bifurc. Chaos 27, 1730038 (2017)

    Article  Google Scholar 

  3. J.C.D. Cardoso, H.A. Albuquerque, R.M. Rubinger, Phys. Lett. A 373, 2050 (2009)

    Article  ADS  Google Scholar 

  4. G.M. Ramírez-Ávila, J.A.C. Gallas, Phys. Lett. A 375, 143 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  5. J.A.C. Gallas, Phys. Rev. Lett. 70, 2714 (1993)

    Article  ADS  Google Scholar 

  6. R. Vitolo, P. Glendinning, J.A.C. Gallas, Phys. Rev. E 84, 016216 (2011)

    Article  ADS  Google Scholar 

  7. W. Façanha, B. Oldeman, L. Glass, Phys. Lett. A 377, 1264 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  8. E. Lorenz, Physica D 237, 1689 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  9. H.A. Albuquerque, R.M. Rubinger, P.C. Rech, Phys. Lett. A 372, 4793 (2008)

    Article  ADS  Google Scholar 

  10. R. Stoop, P. Benner, Y. Uwate, Phys. Rev. Lett. 105, 074102 (2010)

    Article  ADS  Google Scholar 

  11. C. Manchein, H.A. Albuquerque, L.F. Mello, Int. J. Bifurc. Chaos 28, 1830038 (2018)

    Article  Google Scholar 

  12. A.C.C. Horstmann, H.A. Albuquerque, C. Manchein, Eur. Phys. J. B 90, 96 (2017)

    Article  ADS  Google Scholar 

  13. J.A.C. Gallas, Mod. Phys. Lett. B 29, 1530018 (2015)

    Article  ADS  Google Scholar 

  14. J.A.C. Gallas, in Advances in Atomic, Molecular, and Optical Physics, edited by E. Arimondo, C.C. Lin, S.F. Yelin (Elsevier Science, 2016), Vol. 65, Chap. 3, p. 127

  15. A. Celestino, C. Manchein, H.A. Albuquerque, M.W. Beims, Phys. Rev. Lett. 106, 234101 (2011)

    Article  ADS  Google Scholar 

  16. E.S. Medeiros, S.L.T. Souza, R.O. Medrano-T, I.L. Caldas, Chaos Solitons Fractals 44, 982 (2011)

    Article  ADS  Google Scholar 

  17. D.F.M. Oliveira, E.D. Leonel, Chaos 21, 043122 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  18. R.E. Francke, T. Pöschel, J.A.C. Gallas, Phys. Rev. E 87, 042907 (2013)

    Article  ADS  Google Scholar 

  19. C. Manchein, A. Celestino, M.W. Beims, Phys. Rev. Lett. 110, 114102 (2013)

    Article  ADS  Google Scholar 

  20. D.F.M. Oliveira, E.D. Leonel, Physica A 413, 493 (2014)

    Article  ADS  Google Scholar 

  21. G.A. Leonov, N.V. Kuznetsov, Phys. Lett. A 375, 2230 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  22. G.A. Leonov, N.V. Kuznetsov, Int. J. Bifurc. Chaos 23, 1330002 (2013)

    Article  Google Scholar 

  23. A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  24. M. Chen, J.J. Yu, B.C. Bao, Electron. Lett. 51, 462 (2015)

    Article  Google Scholar 

  25. G.A. Leonov, N.V. Kuznetsov, T.N. Mokaev, Eur. Phys. J. Special Topics 224, 1421 (2015)

    Article  ADS  Google Scholar 

  26. G.A. Leonov, N.V. Kuznetsov, T.N. Mokaev, Commun. Nonlinear Sci. Numer. Simul. 28, 166 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  27. R.M. da Silva, C. Manchein, M.W. Beims, Chaos 27, 103101 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  28. C. Manchein, R.M. da Silva, M.W. Beims, Chaos 27, 081101 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  29. R.M. da Silva, C. Manchein, M.W. Beims, Physica A 508, 454 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn, Meccanica 15, 09 (1980)

    Article  ADS  Google Scholar 

  31. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  32. E.S. Medeiros, S.L.T. Souza, R.O. Medrano-T, I.L. Caldas, Phys. Lett. A 374, 2628 (2010)

    Article  ADS  Google Scholar 

  33. R.M. da Silva, N.S. Nicolau, C. Manchein, M.W. Beims, Phys. Rev. E 98, 002200 (2018)

    Google Scholar 

  34. D.R. da Costa, M. Hansen, G. Guarise, R.O. Medrano-T, E.D. Leonel, Phys. Lett. A 380, 1610 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  35. F.F.G. de Sousa, R.M. Rubinger, J.C. Sartorelli, H.A. Albuquerque, M.S. Baptista, Chaos 26, 083107 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  36. A. Dhooge, W. Govaerts, Y.A. Kuznetsov, ACM Trans. Math. Softw. 29, 141 (2003)

    Article  Google Scholar 

  37. R. Barrio, F. Blesa, A. Dena, S. Serrano, Comput. Math. Appl. 62, 4140 (2011)

    Article  MathSciNet  Google Scholar 

  38. R. Barrio, F. Blesa, S. Serrano, A. Shilnikov, Phys. Rev. E 84, 035201(R) (2011)

    Article  ADS  Google Scholar 

  39. A. Hoff, J.V. dos Santos, C. Manchein, H.A. Albuquerque, Eur. Phys. J. B 87, 151 (2014)

    Article  ADS  Google Scholar 

  40. Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, 3rd edn. (Sringer-Verlag, New York, 2004)

  41. A.C.M. Siementkowski, P.C. Rech, Chaos 22, 043147 (2012)

    Article  MathSciNet  Google Scholar 

  42. L.A.S. Rosa, F. Prebianca, A. Hoff, C. Manchein, H.A. Albuquerque (2018), submitted to publication

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710, Joinville, Brazil

    Nathan S. Nicolau, Tulio M. Oliveira, Anderson Hoff, Holokx A. Albuquerque & Cesar Manchein

Authors
  1. Nathan S. Nicolau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tulio M. Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anderson Hoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Holokx A. Albuquerque
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Cesar Manchein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cesar Manchein.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nicolau, N.S., Oliveira, T.M., Hoff, A. et al. Tracking multistability in the parameter space of a Chua’s circuit model. Eur. Phys. J. B 92, 106 (2019). https://doi.org/10.1140/epjb/e2019-90749-x

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2019-90749-x

Keywords

Search

Navigation