Skip to main content
SpringerLink
Log in

Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper presents an experimental characterization of the behavior of an analogous version of the Chua’s circuit. The electronic circuit signals are captured using a data acquisition board (DAQ) and processed using LabVIEW environment. The following aspects of the time series analysis are analyzed: time waveforms, phase portraits, frequency spectra, Poincaré sections, and bifurcation diagram. The circuit behavior is experimentally mapped with the parameter variations, where are identified equilibrium points, periodic and chaotic attractors, and bifurcations. These analysis techniques are performed in real-time and can be applied to characterize, with precision, several nonlinear systems.

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

    Book  MATH  Google Scholar 

  5. 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 

  6. Albuquerque, H.A., Rubinger, R.M., Rech, P.C.: Self-similar structures in a 2D parameter-space of an inductorless Chua’s circuit. Phys. Lett. A 372, 4793–4798 (2008)

    Article  Google Scholar 

  7. Rocha, R., Medrano-T, R.: An inductor-free realization of the Chua’s circuit based on electronic analogy. Nonlinear Dyn. 56, 389–400 (2009)

    Article  Google Scholar 

  8. Suneel, M.: Electronic circuit realization of the logistic map. Sadhana 31, 69–78 (2006)

    Article  Google Scholar 

  9. Tse, C.: Experimental techniques for investigating chaos in electronics. In: Chaos in Circuits and Systems, Chap. 18, pp. 367–384. World Scientific, Singapore (2002)

    Chapter  Google Scholar 

  10. 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 

  11. 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 

  12. National Instruments: Getting started with LabVIEW (2007)

  13. National Instruments: LabVIEW fundamentals (2007)

Download references

Author information

Authors and Affiliations

  1. Federal University of Ouro Preto—UFOP/EM/DECAT, Campus Morro do Cruzeiro, 35400-000, Ouro Preto, MG, Brazil

    Ronilson Rocha & Guilherme L. D. Andrucioli

  2. University of São Paulo—USP/Institute of Physics, C-P: 66318, 05508-900, São Paulo, SP, Brazil

    Rene O. Medrano-T

Authors
  1. Ronilson Rocha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guilherme L. D. Andrucioli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rene O. Medrano-T
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ronilson Rocha.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rocha, R., Andrucioli, G.L.D. & Medrano-T, R.O. Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior. Nonlinear Dyn 62, 237–251 (2010). https://doi.org/10.1007/s11071-010-9714-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-010-9714-6

Keywords

Search

Navigation