Abstract
An electronic circuit realization of the logistic difference equation is presented using analog electronics. The behaviour of the realized system is evaluated against computer simulations of the same. The circuit is found to exhibit the entire range of dynamics of the logistic equation: fixed points, periodicity, period doubling, chaos and intermittency. Quantitative measurements of the dynamics of the realized system are presented and are found to be in good agreement with the theoretical values. Some possible applications of such a realization are briefly discussed.
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References
Baker G, Gollub J 1990Chaotic dynamics: An introduction (Cambridge: University Press)
Cong L, Songgeng S 1998 Chaotic frequency hopping sequencesIEEE Trans. Commun. 46: 1433–1437
Galias Z, Maggio G M 2001 Quadrature chaos shift keying: Theory and performance analysis.IEEE Trans. Circuits Syst. -I 48: 1510–1519
Hasler MJ 1987 Electrical circuits with chaotic behaviour.Proc. IEEE 75: 1009–1021
Heidari-Bateni G, McGillem C D 1994 A chaotic direct-sequence spread-spectrum communication system.IEEE Trans. Commun. 42: 1524–1527
Kiers K, Schmidt D 2004 Precision measurements of a simple chaotic circuit.Am. J. Phys. 72: 503–509
Kumar N 1996Deterministic chaos, complex chance out of simple necessity (Hyderabad: Universities Press)
Mandal S 2002Spread spectrum communication using chaotic signals. B. Tech. thesis, Indian Institute of Technology, Kharagpur
Mandal S, Banerjee S 2003 A chaos based spread spectrum communication systemNatl. Conf. Nonlinear Systems and Dynamics, Kharagpur (Also at http://www.cts.iitkgp.ernet.in/∼ncnsd/cd-ncnsd/html/pdf/309-312.pdf)
Matsumoto T 1987 Chaos in electronic circuits.Proc. IEEE 75: 1033–1056
May R 1976 Simple mathematical models with very complicated dynamics.Nature (London) 261:459
Murakoshi K, Morie T, Nagata M, Iwata A 2000 An arbitrary chaos generator core circuit using PWM/PPM signals.IEEE Asia & S. Pacific Design Automation Conf. Yokohama, Japan
Murali K, Sinha S, Ditto W L 2003 Realization of the fundamental NOR gate using a chaotic circuit.Phys. Rev. E68: 1–5
National Semiconductor Corp. 2000 LF198/ LF298/ LF398/ LF198A/ LF398AMonolithic sample-and-hold circuits (Datasheet)
Pethel S D, Corron N J, Underwood Q, Myneni K 2002 Chaos synchronization via the transmission of symbolic information.7th Exp. Chaos Conf., San Diego, California. Also published inAIP Conference Proceedings Vol. 676 (American Institute of Physics)
Sprott J C, Linz S J 2000 Algebraically simple chaotic flows.Int. J. Chaos Theor. Appl. 5
Texas Instruments 2004 MPY634Wide bandwidth precision analog multiplier (Datasheet)
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Suneel, M. Electronic circuit realization of the logistic map. Sadhana 31, 69–78 (2006). https://doi.org/10.1007/BF02703801
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DOI: https://doi.org/10.1007/BF02703801