Analysis and implementation of dynamical system with periodical discrete jumps

• Autorzy: Gotthans T. , Petrzela J.

Warianty tytułu

PL

Analiza i zastosowanie systemu dynamicznego z periodycznymi skokami dyskretnymi

• Języki publikacji: EN

Abstrakty

EN

The novel method for dynamical motion quantification is discussed in this paper. The proposed approach is verified on the cyclically symmetrical vector field with jump functions generating the large state space attractors recently discovered by the authors. The core part of the calculation engine involves continuous Fourier transform and Cartesian to spherical conversion. It turns out that the existing methods give the incorrect results, have huge demands on the computer performance or completely fail to converge in the finite time. The fully analog as well as hybrid circuitry implementation using off-the-shelf components is also presented and validated by means of the network simulator Orcad Pspice.

PL

W artykule opisano nową metodę dynamicznego kwantowania ruchu. Zasadniczą część obliczeń stanowi transformata Fouriera i sferyczna konwersja Kartezjańska. Założenia potwierdzają symulacje Pspice.

Słowa kluczowe

EN

analog oscillator; dynamical system; chaos; Lyapunov exponents

PL

system dynamiczny kwantowania ruchu; chaos; generator analogowy

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2013
• Tom: R. 89, nr 1a
• Strony: 156--163
• Opis fizyczny: Bibliogr. 17 poz., rys., schem.

Twórcy

autor

Gotthans T.

• Department of Radio Electronics, Brno University of Technology
• ESYCOM, ESIEE Paris, Université Paris-Est

autor

Petrzela J.

• Department of Radio Electronics, Brno University of Technology

Bibliografia

• [1] Petrzela, J., Gotthans, T., Hrubos, Z., Analog implementation of Gotthans-Petrzela oscillator with virtual equilibria. In Proceedings of 21st International Conference Radioelektronika 2011, Brno (Czech Republic), p. 53 – 56.
• [2] Sprott, J. C., Chlouverakis, K. E. Labyrinth chaos. International Journal of Bifurcation and Chaos, 2007, vol. 17, no. 6, p. 2097 – 2108.
• [3] Grygiel, K., Szlachetka, P. Lyapunov exponents analysis of autonomous and nonautonomous set of ordinary differential equations. Acta Physica Polonica B, 1995, vol. 26, no. 8, pp. 1321 – 1331.
• [4] Petrzela, J. Modeling of the strange behavior in the selected nonlinear dynamical systems, part II: analysis. VUTIUM Press, 2010.
• [5] Hentschell, H. G. E., Procaccia, I. The infinite number of generalized dimensions of fractals and strange attractors. Physica D, 1983, vol. 8, p. 435 – 444.
• [6] Grassenberger, P., Procaccia, I. Characterization of strange attractors. Physical Review Letters, 1983, vol. 50, p. 346 – 349.
• [7] Sprott, J. C., Chaos and time series analysis. Oxford University Press, 2003.
• [8] Wolf, A., Swift, J. B., Swinney, H. L., Vastano, J. A. Determining Lyapunov exponents from a time series. Physica 16D, 1985, p. 285 – 317.
• [9] Spany, V., Galajda, P., Guzan, M., Pivka, L., Olejar, M. Chua’s singularities: great miracle in circuit theory. International Journal of Bifurcation and Chaos, 2010, vol. 20, no. 10, pp. 2993 – 3006.
• [10] Barry, N. Treatise on trigonometric series. The Macmillan Company, New York, 1964.
• [11] Itoh, M. Synthesis of topologically conjugate chaotic nonlinear circuits. International Journal of Bifurcation and Chaos, 1997, vol. 7, no. 6, p. 1195 – 1223.
• [12] Itoh, M. Synthesis of electronic circuits for simulating nonlinear dynamics. International Journal of Bifurcation and Chaos, 2001, vol. 11, no. 3, p. 605 – 653.
• [13] Petrzela, J. Modeling of the strange behavior in the selected nonlinear dynamical systems, part I: oscillators. VUTIUM Press, 2008.
• [14] Biolek, D., Senani, R., Biolkova, V., Kolka, Z. Active elements for analog signal processing: classification, review and future perspectives. Radioengineering, 2008, vol. 17, no. 4, p. 15 – 32.
• [15] Petrzela, J., Hrubos, Z., Gotthans, T. Modeling deterministic chaos using electronic circuits. Radioengineering, 2011, vol. 20, no. 2, p. 438 – 444.
• [16] Morters, P., Peres, Y. Brownian motion. Cambridge University Press, 416 pages, 2008.
• [17] Ocampo, H., Paycha, S., Reyes, A. Geometric methods for quantum theory. World Scientific, 530 pages, 2008.