Abstract
We have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistor
We have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistor
L. O. Chua, “Chua's circuit: ten years later,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E77-A, no. 11, pp. 1811–1822, 1994.
View at: Google ScholarG.-P. Jiang, W. K.-S. Tang, and G. Chen, “A simple global synchronization criterion for coupled chaotic systems,” Chaos, Solitons and Fractals, vol. 15, no. 5, pp. 925–935, 2003.
View at: Publisher Site | Google ScholarJ. Zhang, C. Li, H. Zhang, and J. Yu, “Chaos synchronization using single variable feedback based on backstepping method,” Chaos, Solitons and Fractals, vol. 21, no. 5, pp. 1183–1193, 2004.
View at: Publisher Site | Google ScholarM. T. Yassen, “Adaptive control and synchronization of a modified Chua's circuit system,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 113–128, 2003.
View at: Publisher Site | Google ScholarT. Wu and M.-S. Chen, “Chaos control of the modified Chua's circuit system,” Physica D: Nonlinear Phenomena, vol. 164, no. 1-2, pp. 53–58, 2002.
View at: Publisher Site | Google ScholarC.-C. Hwang, H.-Y. Chow, and Y.-K. Wang, “A new feedback control of a modified Chua's circuit system,” Physica D: Nonlinear Phenomena, vol. 92, no. 1-2, pp. 95–100, 1996.
View at: Publisher Site | Google ScholarK. Li, Y. C. Soh, and Z. G. Li, “Chaotic cryptosystem with high sensitivity to parameter mismatch,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 4, pp. 579–583, 2003.
View at: Publisher Site | Google ScholarZ. Li, K. Li, C. Wen, and Y. C. Soh, “A new chaotic secure communication system,” IEEE Transactions on Communications, vol. 51, no. 8, pp. 1306–1312, 2003.
View at: Publisher Site | Google ScholarE. P. dos Santos, M. S. Baptista, and I. L. Caldas, “Dealing with final state sensitivity for synchronous communication,” Physica A: Statistical Mechanics and Its Applications, vol. 308, no. 1–4, pp. 101–112, 2002.
View at: Publisher Site | Google ScholarL. O. Chua, “Chua's circuit: an overview ten years later,” Journal of Circuits Systems and Computers, vol. 4, no. 2, pp. 117–159, 1994.
View at: Publisher Site | Google ScholarL. P. Shil'nikov, “Chua's circuit: rigorous results and future problems,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 10, pp. 784–786, 1993.
View at: Publisher Site | Google ScholarC. Letellier, G. Gouesbet, and N. F. Rulkov, “Topological analysis of chaos in equivariant electronic circuits,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 6, no. 12B, pp. 2531–2555, 1996.
View at: Publisher Site | Google ScholarD. M. Maranhão and C. P. C. Prado, “Evolution of chaos in the Matsumoto-Chua circuit: a symbolic dynamics approach,” Brazilian Journal of Physics, vol. 35, no. 1, pp. 162–169, 2005.
View at: Google ScholarS. Kahan and A. C. Sicardi-Schifino, “Homoclinic bifurcations in Chua's circuit,” Physica A: Statistical Mechanics and Its Applications, vol. 262, no. 1-2, pp. 144–152, 1999.
View at: Publisher Site | Google ScholarT. Matsumoto, L. O. Chua, and K. Ayaki, “Reality of chaos in the double scroll circuit: a computer-assisted proof,” IEEE Transactions on Circuits and Systems, vol. 35, no. 7, pp. 909–925, 1988.
View at: Publisher Site | Google ScholarL. A. B. Tôrres and L. A. Aguirre, “Inductorless Chua's circuit,” Electronics Letters, vol. 36, no. 23, pp. 1915–1916, 2000.
View at: Publisher Site | Google ScholarH. Kantz and T. Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, UK, 1997.
A. F. Gribov and A. P. Krishchenko, “Analytical conditions for the existence of a homoclinic loop in Chua circuits,” Computational Mathematics and Modeling, vol. 13, no. 1, pp. 75–80, 2002.
View at: Publisher Site | Google ScholarA. M. Fraser and H. L. Swinney, “Independent coordinates for strange attractors from mutual information,” Physical Review A, vol. 33, no. 2, pp. 1134–1140, 1986.
View at: Publisher Site | Google ScholarM. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Physical Review A, vol. 45, no. 6, pp. 3403–3411, 1992.
View at: Publisher Site | Google ScholarT. Wu and M.-S. Chen, “Chaos control of the modified Chua's circuit system,” Physica D: Nonlinear Phenomena, vol. 164, no. 1-2, pp. 53–58, 2002.
View at: Publisher Site | Google ScholarM. Sano and Y. Sawada, “Measurement of the Lyapunov spectrum from a chaotic time series,” Physical Review Letters, vol. 55, no. 10, pp. 1082–1085, 1985.
View at: Publisher Site | Google ScholarJ. Kaplan and J. Yorke, “Chaotic behavior of multidimensional difference equations,” in Functional Differential Equations and Approximation of Fixed Points, H. O. Peitgen and H. O. Walther, Eds., Springer, New York, NY, USA, 1987.
View at: Google ScholarR. Radii and A. Politi, “Statistical description of chaotic attractors: the dimension function,” Journal of Statistical Physics, vol. 40, no. 5-6, pp. 725–750, 1985.
View at: Publisher Site | Google ScholarJ. P. Eckmann and D. Ruelle, “Ergodic theory of chaos and strange attractors,” Reviews of Modern Physics, vol. 57, no. 3, pp. 617–656, 1985.
View at: Publisher Site | Google Scholar