Skip to main content
SpringerLink
Log in

On the analysis of semiconductor diode-based chaotic and hyperchaotic generators—a case study

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

Abstract

This paper deals with the mathematical modeling and bifurcation analysis of a class of semiconductor diode-based chaotic and hyperchaotic generators. The simple 4D hyperchaotic electronic oscillator introduced by Tamasevicius et al. (referred to as the TNC oscillator hereafter) is considered as a prototype/paradigm. In contrast to current approaches based on piecewise-linear methods, we propose a smooth mathematical model (with exponential nonlinearity) to investigate the dynamics of the oscillator. Various methods for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, and phase portraits are exploited to establish the connection between the system parameters and various complicated dynamics (e.g., hyperchaos, coexistence of attractors, and transient chaos) of the TNC oscillator. The transitions to hyperchaos are contrasted with equivalent scenarios obtained from an experimental implementation of the circuit. Using bifurcation diagrams as arguments, the analysis reveals/suggests that the Shockley diode model is appropriate for these types of circuits as it provides a close-form (i.e., accurate) description of the system’s dynamics and thus represents an interesting tool for design engineers.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Tamasevicius, A., Namajunas, A., Cenys, A.: Simple 4D chaotic oscillator. Electron. Lett. 32(11), 957–958 (1996)

    Article  Google Scholar 

  2. Tamasevicius, A., Cenys, A., Mykolaitis, G., Namajunas, A., Lindberg, E.: Hyperchaotic oscillators with gyrators. Electron. Lett. 33(7), 542–544 (1997)

    Article  Google Scholar 

  3. Tamasevicius, A., Cenys, A.: Hyperchaos in dynamical systems with a monoactive degree of freedom. Chaos Solitons Fractals 9(1–2), 115–119 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Murali, K., Tamasevicius, A., Mykolaitis, G., Namajunas, A., Lindberg, E.: Hyperchaos system with unstable oscillators. Nonlinear Phenom. Complex Syst. 3, 7–10 (2000)

    Google Scholar 

  5. Barbara, C., Silvano, C.: Hyperchaotic behaviour of two bi-directionally Chua’s circuits. Int. J. Circuit Theory Appl. 30, 625–637 (2002)

    Article  MATH  Google Scholar 

  6. Cenys, A., Tamasevicius, A., Baziliauskas, A., Krivickas, R., Lindberg, E.: Hyperchaos in coupled Colpitts oscillators. Chaos Solitons Fractals 17, 349–353 (2003)

    Article  MATH  Google Scholar 

  7. Matsumoto, T., Chua, L.O., Kobayashi, K.: Hyperchaos: laboratory experiment and numerical confirmation. IEEE Trans. Circuits Syst. 11, 1143–1147 (1986)

    Article  MathSciNet  Google Scholar 

  8. Effati, S., Saberi Nik, H.: Hyperchaos control of the hyperchaotic chen system by optimal control design. Nonlinear Dyn. 73, 499–508 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Rossler, O.E.: An equation for hyperchaos. Phys. Lett. A 71, 155–157 (1979)

    Article  MathSciNet  Google Scholar 

  10. Keihui, S., Xuan, L., Cong, Z., Sprott, J.C.: Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system. Nonlinear Dyn. 69, 1383–1391 (2012)

    Article  Google Scholar 

  11. Mykolaitis, G., Tamasevicius, A., Cenys, A., Bumeliene, S., Anagnostopoulos, A.N., Kalkan, N.: Very high and ultrahigh frequency hyperchaotic oscillators with delay line. Chaos Solitons Fractals 17, 343–347 (2003)

    Article  MATH  Google Scholar 

  12. Hanias, M.P., Giannaris, G., Spyridakis, A.: Rigas: time series analysis in chaotic diode resonator circuit. Chaos Solitons Fractals 27, 569–573 (2006)

    Article  MATH  Google Scholar 

  13. Kengne, J., Chedjou, J.C., Kenne, G., Kyamakya, K.: Dynamical properties and chaos synchronization of improved Colpitts oscillators. Commun. Nonlinear Sci. Numer. Simul. 17, 2914–2923 (2012)

    Article  MathSciNet  Google Scholar 

  14. Kengne, J., Chedjou, J.C., Fono, V.A., Kyamakya, K.: On the analysis of bipolar transistor based chaotic circuits: case of a two-stage Colpitts oscillator. Nonlinear Dyn. 67, 1247–1260 (2012)

    Article  Google Scholar 

  15. Maggio, G.M., Di Bernardo, M., Kennedy, M.P.: Nonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillator. IEEE Trans. Circuits Syst. I 47, 1160–1177 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ueta, T., Tamura, A.: Bifurcation analysis of a simple 3D oscillator and chaos synchronization of its coupled systems. Chaos Solitons Fractals 45, 1460–1468 (2012)

    Google Scholar 

  17. Maggio, G.M., De Feo, O., Kennedy, M.P.: Nonlinear analysis of the Colpitts oscillator and application to design. IEEE Trans. Circuits Syst. I 46, 1118–1130 (1999)

    Article  MATH  Google Scholar 

  18. Damon, A.M., Grassi, G.: Experimental realization of observer-based hyperchaos synchronization. IEEE Trans. Circuits Syst. I 48(3), 366–374 (2001)

    Article  Google Scholar 

  19. Tamasevicius, A., Mykolaitis, G., Cenys, A., Namajunas, A.: Synchronization of 4D hyperchaotic oscillators. Electron. Lett. 32(17), 1536–1538 (1996)

    Article  Google Scholar 

  20. Tamasevicius, A., Cenys, A.: Synchronizing hyperchaos with a single variable. Phys. Rev. E 55(1), 297–299 (1997)

    Article  Google Scholar 

  21. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. 40(10), 626–633 (1993)

    Article  Google Scholar 

  22. Tamasevicius, A., Cenys, A., Mykolaitis, G.: Driving nonlinear resonator with hyperchaotic signals. Electron. Lett. 32(22), 2029–2030 (1996)

    Article  Google Scholar 

  23. Balanov, A., Janson, N., Postnov, D., Sosnovtseva, O.: Synchronization: From Simple to Complex. Springer, Berlin (2009)

    Google Scholar 

  24. Buscarino, A., Fortuna, L., Frasca, M.: Experimental robust synchronization of hyperchaotic circuits. Phys. D 238(18), 1917–1922 (2009)

    Article  MATH  Google Scholar 

  25. Yang, T.: A survey of chaotic secure communication systems. Int. J. Comput. Cognit. 2(2), 81–130 (2004)

    Google Scholar 

  26. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Field. Springer, New York (1983)

    Book  Google Scholar 

  27. Bennettin, G., Galgani, L., Strelcyn, J.M.: Kolgoromov entropy and numerical experiments. Phys. Rev. A 14, 2338–2345 (1993)

    Article  Google Scholar 

  28. Masoller, C.: Coexistence of attractors in a laser diode with optical feedback from a large external cavity. Phys. Rev. A 50, 2569–2578 (1994)

    Article  Google Scholar 

  29. Cushing, J.M., Henson, S.M., Blackburn, : Multiple mixed attractors in a competition model. J. Biol. Dyn. 1(4), 347–362 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  30. Vaithianathan, V., Veijun, J.: Coexistence of four different attractors in a fundamental power system model. IEEE Trans. Circuits Syst. I 46(3), 405–409 (1999)

    Article  Google Scholar 

  31. Buscarino, A., Fortuna, L., Frasca, M., Sciuto, G.: Chaos control in inductor-based chaotic oscillators. In: Proceedings of the 19\({{\rm th}}\) International Symposium on Mathematical Theory of Networks-MTNS2010, pp. 2207–2210. Budapest, Hungry, 5–9 July 2010

  32. Paula, A.S., Savi, M.A., Peireira-Pinto, F.H.: Chaos and transient chaos in an experimental nonlinear pendulum. J. Sound Vib. 294, 585–595 (2006)

    Article  Google Scholar 

  33. Izrailev, F.M., Timmermann, B., Timmermann, W.: Transient chaos in a generalized Henon map on the torus. Phys. Lett. A 126, 405–410 (1988)

    Google Scholar 

  34. Nayfeh, A.H.: Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods. Wiley, New York (1995)

    Book  MATH  Google Scholar 

  35. Yang, X.S., Yuan, Q.: Chaos and transient chaos in simple Hopfield neural network. Neurocomputing 69, 232–241 (2005)

    Article  Google Scholar 

  36. Yorke, J.A., Yorke, E.D.: The transition to sustained chaotic behavior in the Lorenz model. J. Stat. Phys. 21, 263–277 (1979)

    Article  MathSciNet  Google Scholar 

  37. Itoh, M.: Synthesis of electronic circuits for simulating nonlinear dynamics. Int. J. Bifurc. Chaos 11(3), 605–653 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire d’Automatique et Informatique Apliquée (LAIA), IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon

    J. Kengne, T. Fonzin Fozin & G. Kenne

  2. Laboratoire d’Electronique, Faculté de Sciences, Université de Dschang, Dschang, Cameroon

    T. Fonzin Fozin

  3. Institute for Smart- Systems Technologies, University of Klagenfurt, Klagenfurt, Austria

    J. Kengne, J. C. Chedjou & K. Kyamakya

Authors
  1. J. Kengne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. C. Chedjou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Fonzin Fozin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Kyamakya
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. Kenne
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Kengne.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kengne, J., Chedjou, J.C., Fonzin Fozin, T. et al. On the analysis of semiconductor diode-based chaotic and hyperchaotic generators—a case study. Nonlinear Dyn 77, 373–386 (2014). https://doi.org/10.1007/s11071-014-1301-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1301-9

Keywords

Search

Navigation