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Novel circuit implementation of universal and fully analog chaotic oscillator

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Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
PL
Nowy układ uniwersalnego, analogowego generatora przebiegów chaotycznych
Języki publikacji
EN
Abstrakty
EN
It has been shown that the so-called dynamical system of class C can be used for studying chaotic motions. Even though we are speaking about a deterministic dynamical systems, theirs future evolution can hardly be predicted. It is due to the extreme sensitivity on tiny changes in the initial conditions. Everything follows from the general theory of the chaotic dynamics – one must have a large number of unstable initial conditions. This also suggests that a little change in the values of variable parameters can cause a dramatic change of the state space attractor’s shape. This was also the main motivations to the construction of the optimized dynamical system of class C with piecewise-linear (PWL) feedback. Based on the given system of first-order differential equations, a fully analog chaotic oscillator works in hybrid mode has been discovered for laboratory measurements. Main contribution of this work is right in circuitry implementation of a fully analog chaotic oscillator with a new available active elements. The advantage is immediately evident. The smaller number of active elements is in the whole circuit. The proper function of the final circuit structure has been verified by means of the PSpice simulator as well as by a practical experiments on the real oscillator. The corresponding results are also given.
PL
Tak zwany dynamiczny system klasy C może być użyty do studiowania procesów chaotycznych. W pracy do badań zastosowano system klasy C z liniowym sprzężeniem zwrotnym PWL. Uzyskano analogowy generator przebiegów chaotycznych. Zaletą jego jest mała liczba elementów aktywnych. Układ sprawdzono eksperymentalnie i przez symulacje.
Rocznik
Strony
18--22
Opis fizyczny
Bibliogr. 18 poz., il., schem., tab.
Twórcy
autor
  • Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, ul. Purkynova 118, 612 00 Brno, Czech Republic, xhrubo00@stud.feec.vutbr.cz
Bibliografia
  • [1] Biolek D., Senani R., Biolkova V., Kolka Z.: Active elements for analog signal processing: Classification, Review, and New Proposal, Radioengineering, 17(4), pp. 14–32, 2008.
  • [2] Kolka Z.: Synthesis of Optimized Piecewise-Linear Systems Using Similarity Transformation, Part I: Basic Principles, Radioengineering, 10(3), pp. 5–7, 2001.
  • [3] Pospisil J., Kolka Z., Horska J.: Synthesis of Optimized Piecewise-Linear Systems Using Similarity Transformation, Part II: Second-Order Systems, Radioengineering, 10(3), pp. 8–10, 2001.
  • [4] Pospisil J., Kolka Z., Hanus S., Brzobohaty J.: Synthesis of Optimized Piecewise-Linear Systems Using Similarity Transformation, Part III: Second-Order Systems, Radioengineering, 11(2), pp. 11–13, 2002.
  • [5] Pospisil J., Brzobohaty J., Kolka Z., Horska J.: ecomposed Canonical State Models of the Third-Order Piecewise-Linear Dynamical Systems, ECCTD’99,, pp. 181–184, 1999.
  • [6] Chua L., Komuro M., Matsumoto T.: The Double Scroll Family, IEEE Trans. on CAS I: Fundamental Theory and Applications, vol. 33, no. 11, 1986, ISSN 0098-4094.
  • [7] Sprott J. C.: Chaos and Time-Series Analysis, Oxford University Press, 507 pages, 2003, ISBN 01-985-0840-9.
  • [8] Kennedy M. P.,: Three steps to chaos-part II: A Chua’s circuit primer, IEEE Trans. on CAS I: Fundamental theory and applications, vol. 40, no. 10, pp. 657–674, 1993.
  • [9] Thompson J.M.T., Stewart H.B.: Nonlinear dynamics and chaos, Wiley; 2nd edition, 560 pages, 2002, ISBN 04-718-7684-4.
  • [10] Itoh M.: Synthesis of Electronic Circuit for Simulating Nonlinear Dynamics, International Journal of Bifurcation and Chaos, 11(3), pp. 605–653, 2001.
  • [11] Fujisaka H., Sato Ch.: Computing the Number, Location, and Stability of Fixed Points of Poincaré Maps, IEEE Trans. on CAS I: Fundamental Theory and Applications , vol. 44, no. 4, 1997, ISSN 1057–7122.
  • [12] Ueta T., Kawakami H., Yoshinaga T., Katsuta Y.: A computation of Bifurcation Parameter Values for Limit Cycles, IEEE International Symposium on Circuits and Systems, pp. 801– 804, June 9-12 1997.
  • [13] Katsuta Y., Kawakami H.: Bifurcations of Equilibriums and Periodic Solutions in Nonlinear Autonomous System with Symmetry, IEICE Trans. J75-A, 6, pp. 1035-1044, 1992.
  • [14] Petrzela J.: Modeling of the Strange Behavior in the Selected Nonlinear Dynamical Systems,Part II: Analysis, Brno: Vutium Press, 2010.
  • [15] Petrzela J., Gotthans T.: Chaotic Oscillators with Single Polynomial Nonlinearity and Digital Sampled Dynamics, Przeglad Elektrotechniczny, vol. 3, no. 1, pp. 161–163, 2011.
  • [16] Petrzela J., Gotthans T., Hrubos Z.: Modeling deterministic chaos using electronic circuits, Radioengineering, vol. 20, no. 2, pp. 438–444, 2011.
  • [17] Analog Devices: Monolithic Op. Amp. AD844, 20p., [web page] http://www.analog.com, [Accessed on 30 Sept. 2011].
  • [18] Maxim: Wideband Transconductance Amp. MAX435, 17p., [web page] http://www.maxim-ic.com, [Accessed on 30 Sept. 2011].
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPOH-0065-0004
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