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


For citation:

Anishchenko V. S. Attractors of dynamical systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 1, pp. 109-127. DOI: 10.18500/0869-6632-1997-5-1-109-127

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: 0)
Language: 
Russian
Article type: 
Other
UDC: 
537.86

Attractors of dynamical systems

Autors: 
Anishchenko Vadim Semenovich, Saratov State University
Abstract: 

In this lection the definition of an attractor of а dissipative dynamical system is introduced. Classification of existing types of atiractors and analysis of their characterictics are presented. The discussed problems are illustrated by the results of numerical simulation using a number of real examples. This gives the possibility to urflderstzmd easily the main properties, similarities and differences of the considered types of atfractors.

Key words: 
Acknowledgments: 
The work was partially financed by grants from the State Committee for Higher Education of the Russian Federation (95-0-8.3-66) and a joint grant from the Physical Society of Germany (436 RUS 113/334).
Reference: 
  1. Lichtenberg АJ, Lieberman MA. Regular and Stochastic Motion. N.Y.: Springer; 1983. 499 p. DOI: 10.1007/978-1-4757-4257-2.
  2. Schuster G. Deterministic Chaos: An Introduction. Weinheim: Wiley;1998. 270 p.
  3. Anishchenko VS. Complex Oscillations in Simple Systems. М.: Nauka; 1990. 312 p. (in Russian).
  4. Afraimovich VS. Ring principle and quasi-attractors. In: Proc. of the International Conference on Nonlinear Oscillations. Vol 2. Kiev: Naukova Dumka; 1984. P. 34. (in Russian).
  5. Lorenz EN. Deterministic non-periodic flow. J. Atm. Sci. 1963;20:130-141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
  6. Ruelle D, Takens F. On the nature of turbulence. Commun.Math. Phys. 19711;20:167-192. DOI: 10.1007/BF01646553.
  7. Shilnikov, LP. Bifurcation theory and the Lorenz model. In: Appendix to Russian edition of Mardsen J, McCraken M, editors. The Hopf Bifurcation and Its Applications. M.: Mir; 1980. P. 317–335.
  8. Anishchenko VS. Dynamical Chaos — Models and Experiments. Singapore: World Scientific; 1995. 400 p.
  9. Rabinovich MI, Trubetskov DI. Introduction to the Theory of Oscillations and Waves. М.: Nauka; 1984. 432 p. (in Russian).
  10. Neimark YuI, Landa PS. Stochastic and Chaotic Osciliations. Dordrecht: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
  11. Farmer JD, Ott E, Yorke JA. The dimension of chaotic attractors. Physica D. 1983;7(1-3):153-180. DOI: 10.1016/0167-2789(83)90125-2.
  12. Grebogi C, Ott E, Pelikan S, Yorke JA. Strange attractors that are not chaotic. Physica D. 1984;13(1-2):261-268. DOI: 10.1016/0167-2789(84)90282-3.
Received: 
18.02.1997
Accepted: 
19.03.1997
Published: 
18.05.1997