Skip to main content
Log in

On classification and special features of motion of dynamic systems

  • Published:
Russian Physics Journal Aims and scope

Abstract

A number of debatable problems of modern nonlinear physics are discussed. A classification of deterministic systems with chaotic behavior by the degree of openness and type of motion is suggested. Examples of dynamic systems illustrating the consistency of this classification are presented, and special features of functioning of these systems and problems of quantitative estimation of the degree of randomness are considered. A strict definition of quasi-deterministic chaos is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. L. Ginzburg, Usp. Fiz. Nauk, 169, No. 4, 419–441 (1999).

    Article  MathSciNet  Google Scholar 

  2. G. M. Zaslavskii and R. Z. Sagdeev, Introduction to Nonlinear Physics [in Russian], Nauka, Moscow (1988).

    MATH  Google Scholar 

  3. F. C. Moon, Chaotic Vibrations [Russian translation], Mir, Moscow (1990).

    MATH  Google Scholar 

  4. M. I. Rabinovich and D. I. Trubetskov, Introduction to the Theory of Oscillations and Waves [in Russian], Nauka, Moescow (1984).

    Google Scholar 

  5. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Dynamics [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  6. Yu. I. Neimark and P. S. Landa, Stochastic and Chaotic Fluctuations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  7. S. P. Kuznetsov, Dynamic Chaos [in Russian], Physical and Mathematical Literature Press, Moscow (2001).

    Google Scholar 

  8. M. Tabor, Chaos and Integrability in Nonlinear Dynamics [in Russian], Editorial URSS, Moscow (2001).

    Google Scholar 

  9. A. Yu. Loskutov and A. S. Mikhailov, Introduction to Synergy [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  10. P. Levi, Stochastic Processes and Brownian Motion [Russian translation], Nauka, Moscow (1972).

    Google Scholar 

  11. S. N. Vladimirov and V. V. Negrul, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Dinam., 9, Nos. 4–5, 64–77 (2001).

    MATH  Google Scholar 

  12. Ya. B. Pesin, Usp. Matem. Nauk, 32, No. 4, 55–112 (1977).

    MathSciNet  Google Scholar 

  13. S. N. Vladimirov, Russ. Phys. J., No. 2, 211–219 (2004).

  14. S. N. Vladimirov and A. A. Shtraukh, Zh. Tekh. Fiz., 74, No. 7, 1–5 (2004).

    Google Scholar 

  15. V. S. Anishchenko, A. B. Neuman, F. Moss, et al., Usp. Fiz. Nauk, 169, No. 1, 7–38 (1999).

    Article  ADS  Google Scholar 

  16. N. V. Evdokimov, V. P. Komolov, and P. V. Komolov, Usp. Fiz. Nauk, 171, No. 7, 775–795 (2001).

    Google Scholar 

  17. S. N. Vladimirov, Usp. Fiz. Nauk, 174, No. 2, 217–220 (2004).

    Google Scholar 

  18. A. A. Stanislavskii, Pis’ma Zh. Tekh. Fiz., 32, No. 4, 1–5 (2006).

    Google Scholar 

  19. I. A. Khovanov, N. A. Khovanova, V. S. Anishchenko, et al., Zh. Tekh. Fiz., 70, No. 5, 112–114 (2000).

    Google Scholar 

  20. S. N. Vladimirov, Russ. Phus. J., No. 4, 375–382 (2005).

  21. M. P. Pokrovskii, Vopr. Filos., No. 7, 95–104 (2006).

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 49–58, November, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vladimirov, S.N. On classification and special features of motion of dynamic systems. Russ Phys J 49, 1204–1214 (2006). https://doi.org/10.1007/s11182-006-0245-z

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11182-006-0245-z

Keywords

Navigation