ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Kuznetsov S. P. An electronic device implementing a strange nonchaotic Hunt–Ott attractor. Izvestiya VUZ. Applied Nonlinear Dynamics, 2019, vol. 27, iss. 2, pp. 61-72. DOI: 10.18500/0869-6632-2019-27-2-61-72

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 157)
Article type: 

An electronic device implementing a strange nonchaotic Hunt–Ott attractor

Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

Topic and aim. The aim of the article is to propose an electronic device representing a non-autonomous dynamical system with a strange nonchaotic attractor insensitive to variation of parameters (with the only limitation that the ratio of the frequencies of the components of the external control driving remains unchanged being equal to a fixed irrational number). Investigated model. A scheme is composed of two self-oscillating elements excited alternately due to the external modulation of parameters, and the excitation phases are transferred from one subsystem to another in such way that on a period of the modulation they are transformed with fulfillment of certain topological properties corresponding to the formal model proposed by Hunt and Ott. Results. The simulation of the operation of the circuit in Multisim software has been carried out, the results of which allow to confirm validity of the attributing the attractor to the Hunt–Ott class. Oscilloscope traces of signals generated by the system, phase portrait of the attractor, diagrams illustrating the topological nature of the transformation for the phases and the nature of the invariant probability density distribution on the attractor are presented. Discussion. From the point of view of possible applications of strange nonchaotic attractors (communication systems, information processing, cryptographic schemes), the robustness of the considered system is an obvious advantage. In terms of methodology, the proposed material may be interesting for teaching undergraduate and graduate students specializing in radiophysics and electronics with principles of design and analyzing systems with complex dynamics. Although the scheme is demonstrated for a low-frequency band (sound frequencies), it obviously allows modification for use in the radio-frequency band.

  1. Grebogi C., Ott E., Pelikan S., Yorke J.A. Strange attractors that are not chaotic // Physica D. 1984. Vol. 13, № 1–2. P. 261–268.
  2. Feudel U., Kuznetsov S., Pikovsky A. Strange Nonchaotic Attractors. Dynamics between Order and Chaos in Quasiperiodically Forced Systems. Singapore: World Scientific, 2006.
  3. Hunt B.R., Ott E. Fractal properties of robust strange nonchaotic attractors // Physicl Review Letters. 2001. Vol. 87, № 25. 254101.
  4. Anosov D.V. Dynamical systems in the 1960s: The hyperbolic revolution. In book: Mathematical Events of the Twentieth Century. Berlin Heidelberg, Springer-Verlag and Moscow, PHASIS, 2006, pp. 1–18. 
  5. Kim J.W., Kim S.Y., Hunt B., Ott E. Fractal properties of robust strange nonchaotic attractors in maps of two or more dimensions // Physical Review E. 2003. Vol. 67, № 3. 036211.
  6. Jalnine A.Yu., Kuznetsov S.P. On the realization of the Hunt–Ott strange nonchaotic attractor in a physical system. Technical Physics, 2007, vol. 52, no. 4, pp. 401–408.
  7. Doroshenko V.M., Kuznetsov S.P. A system governed by a set of nonautonomous differential equations with robust strange nonchaotic attractor of Hunt and Ott type // European Physical Journal. Special Topics. 2017. Vol. 226, № 9. С. 1765–1775.
  8. Herniter M.E. Schematic Capture with Multisim. Prentice Hall, 2004.
  9. Benettin G., Galgani L., Giorgilli A., Strelcyn J.-M. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them // Meccanica. 1980. Vol. 15. P. 9–30.
  10. Kuznetsov S.P. Hyperbolic Chaos: A Physicist’s View. Beijing: Higher Education Press and Berlin, Heidelberg: Springer-Verlag, 2012.
  11. Pikovsky A., Politi A. Lyapunov Exponents: A Tool to Explore Complex Dynamics. Cambridge University Press, 2016.
  12. Pikovsky A.S., Feudel U. Correlations and spectra of strange nonchaotic attractors // J. Phys. A: Math. Gen. 1994. Vol. 27. P. 5209–5219.
  13. Pikovsky A.S., Zaks M.A., Feudel U., Kurths J. Singular continuous spectra in dissipative dynamics // Physical Review E. 1995. Vol. 52, № 1. С. 285–296.
  14. Zhou C., Chen T. Robust communication via synchronization between nonchaotic strange attractors // Europhysics Letters. 1997. Vol. 38, № 4. С. 261–265.
  15. Ramaswamy R. Synchronization of strange nonchaotic attractors // Physical Review E. 1997. Vol. 56, № 6. P. 7294–7296.
  16. Aravindh M.S., Venkatesan A., Lakshmanan M. Strange nonchaotic attractors for computation // Physical Review E. 2018. Vol. 97, № 5. P. 052212.
  17. Rizwana R., Mohamed I.R. Applicability of strange nonchaotic Wien-bridge oscillators for secure communication // Pramana. 2018. Vol. 91, № 1, 10. 
Short text (in English):
(downloads: 157)