NUMERICAL INVESTIGATION OF SIGNAL AMPLIFICATION VIA VIBRATIONAL RESONANCE IN CHUA'S CIRCUIT
DOI:
https://doi.org/10.46881/ajsn.v6i0.138Keywords:
Chua's circuit, Cubic nonlinearity, Vibrational resonance, Phase portraitAbstract
In this paper, we numerically investigated the occurrence of Vibrational Resonance in a modified Chua's oscillator with a smooth nonlinearity, described by a cubic polynomial. Response curves generated from the numerical simulation at the low frequency reveal that the system's response amplitude could be controlled by modulating the conductance parameter of the Chua's circuit, rather modulating the parameters of the fast-periodic force. Modulating the frequency of the fast-periodic force slightly reduces the response amplitude; shifts the peak point to a higher value of the amplitude of the fast-periodic force by widening the resonance curves. Within certain parameter regime of the high frequency (Ω >100ω), the system's response gets saturated, and further increase does not affect its amplitude.References
Abirami, K., Rajasekar, S. and Sanjaun, M.A.F. (2017). Vibrational Resonance in a Harmonically Trapped Potential System,. Commun Nonlinear Sci Numer Simulate, 47:370-378.
Alghassab, M., Mahmoud, A. and Zohdy, M.A. (2017). Nonlinear Control of Chaotic forced Duffing and Van der Pol Oscillators. International Journal of Modern Nonlinear Theory and Application, 6: 26-37.
Benzi, R. Sutera, A. and Vulpiani, A. (1981).The Mechanism of Stochastic Resonance. Journal of Physics A: Mathematical and General, 14(11): 11 L 453-L457
Blekhman, I. and Landa, P. (2004).“Conjugate Resonance and bifurcation in nonlinear systems under biharmonical excitation,”International Journal of nonlinear mechanics,39: 421-426.
Boeing, G. (2016). "Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self Similarity and the Limits of Prediction,". S y s t e m ’ s . 4 ( 4 ) : 3 7 . doi:10.3390/systems4040037.
Chua, L. O. (1994). Chua's circuit: Ten years later, IEICE Trans. Fund. Electron. Comm. Comput. Sci.,77: 1811–1822.
Ekinci, K.L. and Roukes, M.L. (2005).“Nanoelectromechanical Systems,” Review of Scientific Instruments. AIP applied physics letter photonics: An Interdisciplinary Journal of Nonlinear Science,76 (6):061101-0611012.
Enjieu-Kadji, H.G., Chabi-Orou, J.B. and Woafo, P. (2008).“Regular and Chaotic Behaviors of Plasma Oscillations modeled by a Modified Duffing Equation,”Physica Scripta,77:025503.
Gitterman, M. (2001).“Bistable Oscillator Driven by Two Periodic fields,”Journal of Physics A:Mathematical and General,34: L355.
Goldberger A.L., Moody G.B. and Costa M.D., (2012). PhysioBank, PhysioToolkit, and PhysioNet. Tutorial: Variability vs. Complexity. Jan 24, 2012. http://physionet.org/tutorials/cv/
Harry, F. O. (1967).Music, Physics and Engineering. Dover Publications, pp. 248–249.
Hosen, M.A. and Chowdhury, M.S.H. (2015). Analytical Approximate Solutions for the Helmholtz-Duffing Oscillator. ARPN Journal of Engineering and Applied Sciences,10(23): 23.17363-17369
James, H.H. (2004). Electric Power Transformer Engineering. CRC Press. 2–216. ISBN 978-0-8493-1704-0
Jothimurugan, R., Thamilmaran, K., Rajasekar, S., & Sanjuán, M. A. (2013). Experimental evidence for vibrational resonance and enhanced signal transmission in Chua's circuit. International Journal of Bifurcation and Chaos, 23(11): 1350189
Khibnik, A. I., Roose, D., and Chua, L. O. (1993). On periodic orbits and homoclinic bifurcations in Chua's circuit with a smooth nonlinearity, Int. J. Bifurcat. Chaos Appl. Sci. Eng., 3: 363–384.
Landa, P.S. and McClintock, P.V.E. (2000).Vvibrational Rresonance, Journal of Physics A: Mathematical and General, 33: L433-L438.
Michael, H.T. (2006). Electronic Circuits: Fundamentals and Applications. Newness. 77–78. ISBN 978-0-7506-6923-8
Nayfeh, A.H. and Mook, T.R. (1979). Nonlinear Oscillations, New York, Wiley
