Bilinear systems and chaos

Sergej Čelikovský; Antonín Vaněček

Kybernetika (1994)

  • Volume: 30, Issue: 4, page 403-424
  • ISSN: 0023-5954

How to cite

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Čelikovský, Sergej, and Vaněček, Antonín. "Bilinear systems and chaos." Kybernetika 30.4 (1994): 403-424. <http://eudml.org/doc/27317>.

@article{Čelikovský1994,
author = {Čelikovský, Sergej, Vaněček, Antonín},
journal = {Kybernetika},
keywords = {skew-symmetry; eigenvalue; bilinear system; homoclinic orbits; chaotic behavior; numerical simulation},
language = {eng},
number = {4},
pages = {403-424},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bilinear systems and chaos},
url = {http://eudml.org/doc/27317},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Čelikovský, Sergej
AU - Vaněček, Antonín
TI - Bilinear systems and chaos
JO - Kybernetika
PY - 1994
PB - Institute of Information Theory and Automation AS CR
VL - 30
IS - 4
SP - 403
EP - 424
LA - eng
KW - skew-symmetry; eigenvalue; bilinear system; homoclinic orbits; chaotic behavior; numerical simulation
UR - http://eudml.org/doc/27317
ER -

References

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  1. F. Alberting, E. D. Sontag, Some connections between chaotic dynamical systems and control systems, In: Proceedings of First European Control Conference, Grenoble, 1991, pp. 159-163. (1991) 
  2. S. Čelikovský, A. Vaněček, Bilinear systems as the strongly nonlinear systems, In: Systems Structure and Control (V. Strejc, ed.), Pergamon Press, Oxford 1992, pp. 264-267. (1992) 
  3. S. Čelikovský, On the stabilization of homogeneous bilinear systems, Systems and Control Lett. 21 (1993), 6. (1993) MR1249929
  4. W. J. Freeman, Strange attractors that govern mammalian brain dynamics shown by trajectories of EEG potential, IEEE Trans. Circuits and Systems 35 (1988), 791-783. (1988) MR0947807
  5. R. Genesio, A. Tesi, Chaos prediction in nonlinear feedback systems, IEE Proc. D 138 (1991), 313-320. (1991) Zbl0754.93024
  6. R. Genesio, A. Tesi, Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems, Automatica 28 (1992), 531-548. (1992) Zbl0765.93030
  7. R. Genesio, A. Tesi, A harmonic balance approach for chaos prediction: the Chua's circuit, Internat. J. of Bifurcation and Chaos 2 (1992), 61-79. (1992) MR1166315
  8. A. L. Goldberger, Nonlinear dynamics, fractals, cardiac physiology and sudden death, In: Temporal Disorder in Human Oscillatory Systems, Springer-Verlag, Berlin 1987. (1987) MR0901320
  9. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York 1986. (1986) MR1139515
  10. A. V. Holden (ed.), Chaos, Manchester Univ., Manchester 1986. (1986) Zbl0743.58005
  11. H. Hyotyniemi, Postponing chaos using a robust stabilizer, In: Preprints of First IFAC Symp. Design Methods of Control Systems, Pergamon Press, Oxford 1991, pp. 568-572. (1991) 
  12. L. O. Chua (ed.), Special Issue on Chaotic Systems, IEEE Proc. 6 (1987), 8, 75. (1987) 
  13. E. N. Lorenz, Deterministic non-periodic flow, J. Atmospheric Sci. 20 (1965), 130-141. (1965) 
  14. G. B. Di Massi, A. Gombani, On observability of chaotic systems: an example, Realization and Modelling in Systems Theory. In: Proc. International Symposium MTNS-89, Vol. II, Birkhäuser, Boston -- Basel -- Berlin 1990, pp. 489-496. (1990) MR1115421
  15. R. R. Mohler, Bilinear Control Processes, Academic Press, New York 1973. (1973) Zbl0343.93001MR0332249
  16. J. M. Ottino, The mixing of fluids, Scientific Amer. 1989, 56-67. (1989) 
  17. C. T. Sparrow, The Lorenz Equations: Bifurcation, Chaos and Strange Attractors, Springer-Verlag, New York 1982. (1982) MR0681294
  18. A. Vaněček, Strongly nonlinear and other control systems, Problems Control Inform. Theory 20 (1991), 3-12. (1991) MR1102179
  19. A. Vaněček, S. Čelikovský, Chaos synthesis via root locus, IEEE Trans. Circuits and Systems 41 (1994), 1, 54-60. (1994) 
  20. A. Vaněček, S. Čelikovský, Synthesis of chaotic systems, Kybernetika, accepted. 
  21. S. Wiggins, Global Bifurcations and Chaos. Analytical Methods, Springer-Verlag, New York 1988. (1988) Zbl0661.58001MR0956468

Citations in EuDML Documents

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  1. Antonín Vaněček, Sergej Čelikovský, Synthesis of chaotic systems
  2. Sergej Čelikovský, Observer form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization
  3. Volodymyr Lynnyk, Sergej Čelikovský, On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption
  4. Zdeněk Beran, On characterization of the solution set in case of generalized semiflow
  5. Zhen Wang, Wei Sun, Zhouchao Wei, Shanwen Zhang, Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity
  6. Sergej Čelikovský, Volodymyr Lynnyk, Anna Lynnyk, Branislav Rehák, Generalized synchronization in the networks with directed acyclic structure

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