Abstract
Two simple autonomous chaotic electronic circuits have been proposed in this paper. The core of each of the circuits consists of a single amplifier biquad (SAB). We have proposed two configurations of converting this SAB into chaotic oscillators using suitable passive nonlinear element and a storage element in the form of an inductor. The mathematical models of the proposed chaotic circuits have been constructed, which are fourth order autonomous nonlinear differential equations. The behavior of the proposed circuits has been investigated through numerical simulations, Spice-based circuit simulations and electronic hardware experiments and they agree well with each other. It has been found that both the circuits show complex behaviors like bifurcations and chaos for a certain range of circuit parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley, New York (1995)
Ramos, J.S.: Introduction to nonlinear dynamics of electronic systems: tutorial. Nonlinear Dyn. 44, 3–14 (2006)
Banerjee, T., Sarkar, B.C.: Chaos, intermittency and control of bifurcation in a ZC2-DPLL. Int. J. Electron. 96(7), 717–731 (2009)
Kennedy, M.P.: Chaos in the Colpitts oscillator. IEEE Trans. Circuits Syst. I, Fundam. Theory App. 41, 771–774 (1994)
Namajunas, A., Tamaševičius, A.: Modified Wien-bridge oscillator for chaos. Electron. Lett. 31, 35–336 (1993)
Elwakil, A.S., Kennedy, M.P.: A semi-systematic procedure for producing chaos from sinusoidal oscillators using diode-inductor and FET-capacitor composites. IEEE Trans. Circuit Syst. I 47, 582–590 (2000)
Elwakil, A.S., Soliman, A.M.: Two twin-T based op amp oscillators modified for chaos. J. Franklin Inst. 335B, 771–787 (1998)
Elwakil, A.S., Kennedy, M.P.: Chaotic oscillators derived from sinusoidal oscillators based on the current feedback op amp. Analog Integr. Circuits Signal Process. 24, 239–251 (2000)
Tamaševičius, A., Mykolaitis, G., Bumelienė, S., Baziliauskas, A., Krivickas, R., Lindberg, E.: Chaotic colpitts oscillator for the ultrahigh frequency range. Nonlinear Dyn. 44, 1–4 (2006)
Fortuna, L., Frasca, M., Graziani, S.: A chaotic circuit with ferroelectric nonlinearity. Nonlinear Dyn. 44, 55–61 (2006)
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)
Giannakopoulos, K., Deliyannis, T.: A comparison of five methods for studying a hyperchaotic circuit. Int. J. Electron 92(3), 143–159 (2005)
Lindberg, E.: Colpitts, eigenvalues and chaos. In: Proceedings of NDES’97, pp. 262–267. Moscow (1997)
Bumeliene, S., Tamaševičius, A., Mykolaitis, G., Baziliauskas, A., Lindberg, E.: Numerical investigation and experimental demonstration of chaos from two-stage colpitts oscillator in the ultrahigh frequency range. Nonlinear Dyn. 44, 167–172 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Banerjee, T., Karmakar, B. & Sarkar, B.C. Single amplifier biquad based autonomous electronic oscillators for chaos generation. Nonlinear Dyn 62, 859–866 (2010). https://doi.org/10.1007/s11071-010-9768-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-010-9768-5