Advertisement

An autonomous chaotic and hyperchaotic oscillator using OTRA

  • Manoj Joshi
  • Ashish RanjanEmail author
Article
  • 29 Downloads

Abstract

This research paper reports a novel design for third order chaotic and hyperchaotic oscillator with cubic nonlinearity using single operational trans-resistance amplifier (OTRA) and few passive elements. The key nonlinear dynamical characteristics in terms of sensitivity, divergence, equilibrium point and Lyapunov exponent are recorded in this literature. The operational activity of the proposed oscillator based on OTRA is integrated using 0.25 µm TSMC CMOS parameter. For the generation of hyperchaotic oscillator, an external capacitor is added to the third order chaotic oscillator. To justify the theoretical nonlinear dynamics of proposed chaotic oscillator, PSPICE simulation by using CMOS based OTRA and experimental investigation using IC AD844 based OTRA are well implemented.

Keywords

Chaotic and hyperchaotic oscillator Nonlinear dynamics Nonlinear oscillator Operational trans-resistance amplifier (OTRA) 

References

  1. 1.
    Strogatz, S. H. (2014). Nonlinear dynamics and chaos: With applications to physics (2nd ed.). New York: Hachette Book Group.zbMATHGoogle Scholar
  2. 2.
    Banerjee, S. (2010). Chaos synchronization and cryptography for secure communications. In S. Banerjee (Ed.), Applications for encryption. Hershey: IGI Global. Google Scholar
  3. 3.
    Chua, L. O., Wu, C. W., Huang, A., et al. (1993). A universal circuit for studying and generating chaos. I. Routes to chaos. IEEE Transactions on Circuits and System I: Fundamental Theory and Applications, 40(10), 732–744.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Sprott, J. C. (2011). A new chaotic jerk circuit. IEEE Transactions on Circuits and Systems II: Express Briefs, 58(4), 240–243.CrossRefGoogle Scholar
  5. 5.
    Toumazou, C., Lidgey, F. J., & Haigh, D. G. (1990). Analogue IC design: The current-mode approach. London: Peter Peregrinus Ltd.Google Scholar
  6. 6.
    Ferri, G., & Guerrini, N. C. (2003). Low-voltage low-power CMOS current conveyors (1st ed.). London: Kluwer Academic Publishers.Google Scholar
  7. 7.
    Tamaseviius, A., Lindberg, E., & Kirvaitis, R. (2009). Autonomous Duffing–Holmes type chaotic oscillator. Elektronika ir Elektrotechnika, 5, 43–46.Google Scholar
  8. 8.
    Silva, C. R., & Young, A. M. (1998). Implementing RF broadband chaotic oscillators: Design issues and results. In IEEE international symposium on proceedings of the circuits and systems, Monterey, CA (Vol. 4, pp. 489–493).Google Scholar
  9. 9.
    Tamaseviciute, E., Tamasevicius, A., et al. (2008). Analogue electrical circuit for simulation of the Duffing–Holmes equation. Nonlinear Analysis: Modelling and Control, 13(2), 241–252.zbMATHGoogle Scholar
  10. 10.
    Kennedy, M. P. (1992). Robust OP Amp realization of Chua’s circuit. Frequenz, 46(1992), 3–4.Google Scholar
  11. 11.
    Elwakil, A. S., & Kennedy, M. P. (2000). Improved implementation of Chua’s chaotic oscillator using current feedback Op Amp. IEEE Transactions on Circuits and Systems, 47(1), 76–79.CrossRefGoogle Scholar
  12. 12.
    Pandey, N., & Pandey R. (2013). Current mode full-wave rectifier based on a single MZC–CDTA. In Active and passive electronic components, 2013. Google Scholar
  13. 13.
    Kumar, A., & Paul, S. K. (2018). Nth order current mode universal filter using MOCCCIIs. Analog Integrated Circuits and Signal Processing, 95, 181.CrossRefGoogle Scholar
  14. 14.
    Ranjan, R., & Paul, S. K. (2018). CMOS based sinusoidal oscillator using single CCDDCCTA. Analog Integrated Circuits and Signal Processing, 94, 177–193.CrossRefGoogle Scholar
  15. 15.
    Ranjan, A., et al. (2018). A novel Schmitt trigger and its application using a single four terminal floating nullor (FTFN). Analog Integrated Circuits and Signal Processing, 96(7), 455–467.CrossRefGoogle Scholar
  16. 16.
    Gandhi, G. (2006). Improved chua is circuit and its use in hyper chaotic circuit. Analog Integrated Circuit and Signal Processing, 46(2), 173–178.CrossRefGoogle Scholar
  17. 17.
    Kushwaha, A. K., & Paul, S. K. (2016). Chua’s oscillator using operational transresistance amplifier. Revue Roumaine des Sciences Techniques-Serie Electrotechnique et Energetique, 61, 299–303.Google Scholar
  18. 18.
    Kushwaha, A. K., & Paul, S. K. (2016). Inductorless realization of Chua’s oscillator using DVCCTA. Analog Integrated Circuit and Signal Processing, 88, 137–150.CrossRefGoogle Scholar
  19. 19.
    Kennedy, M. P., et al. (2005). A fast and simple implementation of Chua’s oscillator with cubic-like Nonlinearity. International Journal of Bifurcation and Chaos, 15, 1394–1410.Google Scholar
  20. 20.
    Piper, J. R., & Sprott, J. C. (2010). Simple autonomous chaotic circuits. IEEE Transactions on Circuits and Systems—II: Express Briefs, 57(9), 730–734.Google Scholar
  21. 21.
    Tchitnga, R., et al. (2016). Chaos in a single Op-Amp-based jerk circuit: Experiments and simulations. IEEE Transactions on Circuits and Systems II: Fundamental Theory and Applications, 63(3), 239–243.CrossRefGoogle Scholar
  22. 22.
    Liu, J., et al. (2018). An approach for the generation of an nth-order chaotic system with hyperbolic sine. Entropy, 20, 230.MathSciNetCrossRefGoogle Scholar
  23. 23.
    Chunbiao, L., & Sprott, J. C. (2014). Coexisting hidden attractors in a 4-D simplified Lorenz system. International Journal of Bifurcation and Chaos, 24(3), 1450034.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Lorenz, E. N. (1963). Deterministic non-periodic flow simple 4D chaotic oscillator. Journal of Atmospheric Sciences, 20, 130–141.CrossRefGoogle Scholar
  25. 25.
    Mostafa, H., & Soliman, A. M. (2006). A modified realization of the OTRA. Frequenz, 60, 70–76.CrossRefGoogle Scholar
  26. 26.
    Pandey, R., Pandey, N., & Paul S. K. (2014). Signal processing and generating circuits using OTRA as a building block. Retrieved December 23, 2014 from http://shodhganga.inflibnet.ac.in/handle/10603/31644.
  27. 27.
    Zhou, W., Xu, Y., et al. (2008). On dynamics analysis of a new chaotic attractor. Physics Letters, 372(36), 5773–5777.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Jinhu, L., Chen, G., & Zhang, S. (2002). Dynamical analysis of a new chaotic attractor. International Journal of Bifurcation and Chaos, 12(2), 1001–1015.MathSciNetzbMATHGoogle Scholar
  29. 29.
    Nagar, B. C., & Paul, S. K. (2018). Dynamical single OTRA based two-quadrant analog voltage divider. Analog Integrated Circuit and Signal Processing, 94, 161–169.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electronics and Communication EngineeringNational Institute of Technology ManipurImphalIndia

Personalised recommendations