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Exploring an experimental analog Chua’s circuit

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Abstract

In this work we carry out experimental studies of the paradigmatic Chua’s circuit using an approach of the analog computation instead of performing experiments in the canonical circuit. This means that we have built an electronic circuit that integrates (analog computation), in continuous time, the equations of motion of the canonical Chua’s circuit. The equations of motion of the analogical circuit are equivalent to the canonical circuit, so that the dynamical behaviour is the same. With this approach, we successfully obtain an experimental parameter plane using the largest Lyapunov exponent (here named Lyapunov diagram), directly calculated from the experimental time series, with a good precision, so that different types of dynamical behaviours were characterized in this diagram. Results are in very good agreement with numerical simulation with an additional Gaussian noise. The approach by analog computation used here can be extended to a wide range of dynamical systems, once that the analog circuit simulates, by circuitry implementation, the dynamics of these systems from an experimental point of view.

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References

  1. E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

  2. L.O. Chua, J. Circuits Syst. Comput. 4, 117 (1994)

    Article  Google Scholar 

  3. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors (Springer, New York, 1982)

  4. R.N. Madan, Chua’s Circuit: A Paradigm for Chaos (World Scientific, Singapore, 1993)

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

  6. R. Kiliç A Practical Guide for Studying Chua’s Circuits, World Scientific Series on Nonlinear Science: Series A (World Scientific Publishing, Singapore, 2010)

  7. A. Pchelintsev, Numer. Analys. Appl. 7, 159 (2014)

    Article  Google Scholar 

  8. G. Leonov, N. Kuznetsov, N. Korzhemanova, D. Kusakin, Commun. Nonlinear Sci. Numer. Simul. 41, 84 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Xiong, J.C. Sprott, J. Lyu, X. Wang, Int. J. Bifurcat. Chaos. 27, 1750128 (2017)

    Article  Google Scholar 

  10. R.O. Medrano-T, R. Rocha, Int. J. Bifurcat Chaos 24, 1430025 (2014)

    Article  Google Scholar 

  11. T. Singla, P. Parmananda, M. Rivera, Chaos, Solitons Fractals 107, 128 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  12. B. Bao, Q. Li, N. Wang, Q. Xu, Chaos: Interdiscip. J. Nonlinear Sci. 26, 043111 (2016)

    Article  Google Scholar 

  13. M. Chen, Q. Xu, Y. Lin, B. Bao, Nonlinear Dyn. 87, 789 (2017)

    Article  Google Scholar 

  14. B. Bao, H. Wu, L. Xu, M. Chen, W. Hu, Int. J. Bifurcat. Chaos 28, 1850019 (2018)

    Article  Google Scholar 

  15. R.M. da Silva, N.S. Nicolau, C. Manchein, M.W. Beims, Phys. Rev. E 98, 032210 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  16. N.S. Nicolau, T.M. Oliveira, A. Hoff, H.A. Albuquerque, C. Manchein, Eur. Phys. J. B 92, 106 (2019)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  18. D. Dudkowski, S. Jafari, T. Kapitaniak, N. Kuznetsov, G. Leonov, A. Prasad, Phys. Rep. 637, 1 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  19. V. Wiggers, P.C. Rech, Eur. Phys. J. B 91, 144 (2018)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  21. H.A. Albuquerque, P.C. Rech, Int. J. Circuit Theory Appl. 40, 189 (2012)

    Article  Google Scholar 

  22. D. Maranhão, M. Baptista, J. Sartorelli, I. Caldas, Phys. Rev. E 77, 037202 (2008)

    Article  ADS  Google Scholar 

  23. F.F. de Sousa, R.M. Rubinger, J.C. Sartorelli, H.A. Albuquerque, M.S. Baptista, Chaos: Interdiscip. J. Nonlinear Sci. 26, 083107 (2016)

    Article  Google Scholar 

  24. A. Sack, J.G. Freire, E. Lindberg, T. Pöschel, J.A. Gallas, Sci. Rep. 3, 3350 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. C. Cabeza, C.A. Briozzo, R. Garcia, J.G. Freire, A.C. Marti, J.A. Gallas, Chaos, Solitons Fractals 52, 59 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  27. R. Mannella, P. McClintock, Contemp. Phys. 31, 179 (1990)

    Article  ADS  Google Scholar 

  28. R. Rocha, R.O. Medrano-T, Nonlinear Dyn. 56, 389 (2009)

    Article  Google Scholar 

  29. D. Marcondes, G. Comassetto, B. Pedro, J. Vieira, A. Hoff, F. Prebianca, C. Manchein, H.A. Albuquerque, Int. J. Bifurcat. Chaos 27, 1750175 (2017)

    Article  Google Scholar 

  30. R. Rocha, L. Martins-Filho, R.F. Machado, Int. J. Electric. Eng. Educ. 43, 334 (2006)

    Article  Google Scholar 

  31. R. Hegger, H. Kantz, T. Schreiber, Chaos: Interdiscip. J. Nonlinear Sci. 9, 413 (1999)

    Article  Google Scholar 

  32. C. Grebogi, E. Ott, F. Romeiras, J.A. Yorke, Phys. Rev. A 36, 5365 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  33. Y.C. Lai, T. Tél, in Transient Chaos: Complex Dynamics on Finite Time Scales (Springer Science & Business Media, Berlin, 2011), Vol. 173

  34. T. Tél, Chaos: Interdiscip. J. Nonlinear Sci. 25, 097619 (2015)

    Article  Google Scholar 

  35. A. Hoff, D.T. da Silva, C. Manchein, H.A. Albuquerque, Phys. Lett. A 378, 171 (2014)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  37. F. Prebianca, H.A. Albuquerque, M.W. Beims, Phys. Lett. A 382, 2420 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  38. R.L. Honeycutt, Phys. Rev. A 45, 600 (1992)

    Article  ADS  Google Scholar 

  39. R.L. Honeycutt, Phys. Rev. A 45, 604 (1992)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  42. V.T. Pham, C. Volos, T. Kapitaniak, Systems with HiddenAttractors: From Theory to Realization in Circuits (Springer, Berlin, 2017)

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Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Paraná, 81531-980, Curitiba, PR, Brazil

    Flavio Prebianca & Marcus W. Beims

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

    David W. C. Marcondes & Holokx A. Albuquerque

Authors
  1. Flavio Prebianca
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  2. David W. C. Marcondes
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  3. Holokx A. Albuquerque
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  4. Marcus W. Beims
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Correspondence to Marcus W. Beims.

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Prebianca, F., Marcondes, D.W.C., Albuquerque, H.A. et al. Exploring an experimental analog Chua’s circuit. Eur. Phys. J. B 92, 134 (2019). https://doi.org/10.1140/epjb/e2019-100097-4

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  • DOI: https://doi.org/10.1140/epjb/e2019-100097-4

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