Abstract
The present paper reports an inductor-free realization of Chua’s circuit, which is designed by suitably cascading a single amplifier biquad based active band pass filter with a Chua’s diode. The system has been mathematically modeled with three-coupled first-order autonomous nonlinear differential equations. It has been shown through numerical simulations of the mathematical model and hardware experiments that the circuit emulates the behaviors of a classical Chua’s circuit, e.g., fixed point behavior, limit cycle oscillation, period doubling cascade, chaotic spiral attractors, chaotic double scrolls and boundary crisis. The occurrence of chaotic oscillation has been established through experimental power spectrum, and quantified with the dynamical measure like Lyapunov exponents.
Similar content being viewed by others
References
Ogorzalek, M.J.: Chaos and Complexity in Nonlinear Electronic Circuits. World Scientific Series on Nonlinear Science, Series A, vol. 22 (1997)
Ramos, J.S.: Introduction to nonlinear dynamics of electronic systems: Tutorial. Nonlinear Dyn. 44, 3–14 (2006)
Kennedy, M.P., Rovatti, R., Setti, G. (eds.): Chaotic Electronics in Telecommunications. CRC Press, Boca Raton (2000)
Banerjee, T., Sarkar, B.C.: Chaos, intermittency and control of bifurcation in a ZC2-DPLL. Int. J. Electron. 96(7), 717–731 (2009)
Matsumoto, T., Chua, L.O., Komuro, M.: The double scroll. IEEE Trans. Circuits Syst. 32, 797–818 (1985)
Kennedy, M.P.: Three steps to chaos—Part II: A Chua’s circuit primer. IEEE Trans. Circuits Syst. I 40(10), 640–656 (1993)
Morgul, O.: Inductorless realization of Chua’s oscillator. Electron. Lett. 31, 1424–1430 (1995)
Rocha, R., Medrano-T., R.O.: An inductor-free realization of the Chua’s circuit based on electronic analogy. Nonlinear Dyn. 56(4), 389–400 (2009)
Elwakil, A.S., Kennedy, M.P.: Chua’s circuit decomposition: A systematic design approach for chaotic oscillators. J. Franklin Inst. 337, 251–265 (2000)
Elwakil, A.S., Kennedy, M.P.: Generic RC realizations of Chua’s circuit. Int. J. Bifurc. Chaos 10, 1981–1985 (2000)
Kennedy, M.P.: Robust op-amp realization of Chua’s circuit. Frequenz 46, 66–80 (1992)
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)
Cruz, J.M., Chua, L.O.: A CMOS IC nonlinear resistor for Chua’s circuit. IEEE Trans. Circuits Syst. I 39, 985–995 (1992)
Barboza, R., Chua, L.O.: The four-element Chua’s circuit. Int. J. Bifurc. Chaos 18, 943–955 (2008)
Fortuna, L., Frasca, M., Xibilia, M.G.: Chua’s Circuit Implementations: Yesterday, Today, and Tomorrow. World Scientific Series on Nonlinear Science, Series A, vol. 65 (2009)
Kilic, 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 13, 1475–1493 (2003)
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(1–2), 237–251 (2010)
Deliyannis, T.: High-Q factor circuit with reduced sensitivity. Electron. Lett. 4(26), 577–678 (1968)
Friend, J.J.: A single operational-amplifier biquadratic filter section. In: IEEE Int. Symp. Circuit Theory, pp. 189–190 (1970)
Banerjee, T., Karmakar, B., Sarkar, B.C.: Single amplifier biquad based autonomous electronic oscillators for chaos generation. Nonlinear Dyn. 62, 859–866 (2010)
Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley, New York (1995)
Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)
Buscarino, A., Fortuna, L., Frasca, M., Sciuto, G.: Coupled inductors-based chaotic colpitts oscillator. Int. J. Bifurc. Chaos 2, 569–574 (2011)
Viana, E.R., Rubinger, R.M., Albuquerque, H.A., de Oliveira, A.G., Ribeiro, G.M.: High resolution parameter space of an experimental chaotic circuit. Chaos 20, 023110 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Banerjee, T. Single amplifier biquad based inductor-free Chua’s circuit. Nonlinear Dyn 68, 565–573 (2012). https://doi.org/10.1007/s11071-011-0238-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-011-0238-5