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An inductor-free realization of the Chua’s circuit based on electronic analogy

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Abstract

Although literature presents several alternatives, an approach based on the electronic analogy was still not considered for the implementation of an inductor-free realization of the double scroll Chua’s circuit. This paper presents a new inductor-free configuration of the Chua’s circuit based on the electronic analogy. This proposal results in a versatile and functional inductorless implementation of the Chua’s circuit that offers new and interesting features for several applications. The analogous circuit is implemented and used to perform an experimental mapping of a large variety of attractors.

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References

  1. Ditto, W., Munakata, T.: Principles and applications of chaotic systems. Commun. ACM 38, 96–102 (1995)

    Article  Google Scholar 

  2. Yang, S.-K., Chen, C.-L., Yau, H.-T.: Control of chaos in Lorenz system. Chaos Solitons Fractals 13, 767–780 (2002)

    Article  MATH  Google Scholar 

  3. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. II 40, 626–633 (1993)

    Article  Google Scholar 

  4. Kiers, K., Schmidt, D., Sprott, J.C.: Precision measurements of a simple chaotic circuit. Am. J. Phys. 72, 503–509 (2004)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  6. Medrano-T., R.O., Baptista, M.S., Caldas, I.L.: Basic structures of the Shilnikov homoclinic bifurcation scenario. Chaos 15, 33112 (2005)

    Article  MathSciNet  Google Scholar 

  7. Brown, R.: Generalizations of the Chua equations. IEEE Trans. Circuits Syst. I 40, 878–884 (1993)

    Article  MATH  Google Scholar 

  8. Matsumoto, T., Chua, L.O., Komuro, M.: The double scroll. IEEE Trans. Circuits Syst. 32, 797–818 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  9. Matsumoto, T., Chua, L.O., Komuro, M.: The double scroll bifurcations. Int. J. Circuit Theory Appl. 14, 117–146 (1986)

    Article  MathSciNet  Google Scholar 

  10. Zhong, G.O., Ayrom, F.: Experimental confirmation of chaos from Chua’s circuit. Int. J. Circuit Theory Appl. 13, 93–98 (1985)

    Article  Google Scholar 

  11. Kennedy, M.P.: Robust op-amp realization of Chua’s circuit. Frequenz 46, 66–80 (1992)

    Google Scholar 

  12. Senani, R., Gupta, S.S.: Implementation of Chua’s chaotic circuit using current feedback op-amps. Electron. Lett. 34, 829–830 (1998)

    Article  Google Scholar 

  13. Elwakil, A.S., Kennedy, M.P.: Improved implementation of Chua’s chaotic oscillator using current feedback op-amp. IEEE Trans. Circuits Syst. I 47, 289–306 (2000)

    Google Scholar 

  14. Cruz, J.M., Chua, L.O.: A CMOS IC nonlinear resistor for Chua’s circuit. IEEE Trans. Circuits Syst. I 39, 985–995 (1992)

    Article  MATH  Google Scholar 

  15. Morgül, Ö.: Inductorless realization of Chua’s oscillator. Electron. Lett. 31, 1424–1430 (1995)

    Google Scholar 

  16. Weldon, T.P.: An inductorless Double Scroll chaotic circuit. Am. J. Phys. 58, 936–941 (1990)

    Article  Google Scholar 

  17. Tôrres, L.A.B., Aguirre, L.A.: Inductorless Chua’s circuit. Electron. Lett. 36, 1915–1916 (2000)

    Article  Google Scholar 

  18. Cruz, J.M., Chua, L.O.: A CMOS IC chip of Chua’s circuit. IEEE Trans. Circuits Syst. I 40, 614–625 (1993)

    Article  Google Scholar 

  19. Rodriguez-Vazquez, A., Delgado-Restituto, M.: CMOS design of chaotic oscillators using variables: a monolithic Chua’s circuit. IEEE Trans. Circuits Syst. II 40, 596–611 (1993)

    Article  Google Scholar 

  20. Kiliç, R., Çam, U., Alçi, M., Kuntman, H.: Improved realization of mixed-mode chaotic circuit. Int. J. Bifurc. Chaos Appl. Sci. Eng. 12, 1429–1435 (2002)

    Article  Google Scholar 

  21. Kiliç, R.: A comparative study on realization of Chua’s circuit: hybrid realizations of Chua’s circuit combining the circuit topologies proposed for Chua’s diode and inductor elements. Int. J. Bifurc. Chaos Appl. Sci. Eng. 13, 1475–1493 (2003)

    Article  MATH  Google Scholar 

  22. Rocha, R., Martins Filho, L.S., Machado, R.F.: A methodology for teaching of dynamical systems using analogous electronic circuits. Int. J. Electr. Eng. Educ. 43, 334–345 (2006)

    Google Scholar 

  23. Feigenbaum, M.J.: Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 191, 25–52 (1978)

    Article  MathSciNet  Google Scholar 

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Correspondence to Ronilson Rocha.

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Rocha, R., Medrano-T., R.O. An inductor-free realization of the Chua’s circuit based on electronic analogy. Nonlinear Dyn 56, 389–400 (2009). https://doi.org/10.1007/s11071-008-9408-5

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  • DOI: https://doi.org/10.1007/s11071-008-9408-5

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