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Phenomenological approach to construction of attractors

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Abstract

Simple phenomenological principles permitting the construction of systems of differential equations that lead to chaotic attractors and complicated cycles are proposed. The general principles are illustrated by specific examples.

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References

  1. F. C. Moon,Chaotic Vibrations: An Introduction for Applied Scientists and Engineers, Wiley, New York (1987).

    Google Scholar 

  2. P. Bergé, Y. Pomeau, and Ch. Vidal,L'Ordre dans le Chaos, Hermann, Paris (1985).

    Google Scholar 

  3. G. Nicolis and I. Prigogine,Exploring Complexity: An Introduction, W. H. Freeman, New York (1989).

    Google Scholar 

  4. I. Prigogine,From Being to Becoming, W. H. Freeman and Company, San Francisco (1980).

    Google Scholar 

  5. J. Keizer,Statistical Thermodynamics of Nonequilibrium Processes, Springer, New York (1987).

    Google Scholar 

  6. Yu. L. Klimontovich,Turbulent Motion and the Structure of Chaos [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  7. G. M. Zaslavskii, R. Z. Sagdeev, D. A. Usikov, and A. A. Chernikov,Weak Chaos and Quasiregular Structures [in Russian], Nauka, Moscow (1991).

    Google Scholar 

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

    Google Scholar 

  9. H. G. Schuster,Deterministic Chaos: An Introduction, Physik-Verlag, Weinheim (1984).

    Google Scholar 

  10. E. N. Lorenz,J. Atmos. Sci.,20, 130 (1963).

    Google Scholar 

  11. O. E. Rossler,Z. Naturforsch, Teil A,31, 1162 (1976).

    Google Scholar 

  12. O. E. Rossler,Phys. Lett. A,57, 397 (1976).

    Google Scholar 

  13. A. M. Zhabotinskii,Concentration Auto-Oscillations [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  14. P. J. Holmes,Phys. Trans. R. Soc., London, Ser. A,292, 419 (1979).

    Google Scholar 

  15. Van der Pol and Van der Mark,Nature,120, 363 (1927).

    Google Scholar 

  16. M. Henon,Commun. Math. Phys.,50, 69 (1976).

    Google Scholar 

  17. Yu. M. Ivanchenko, A. A. Lisyanskii, and A. É. Filippov,Fluctuation Effects in Systems with Competing Interactions [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  18. A. É. Fillipov,Zh. Obshch. Biol.,45, 410 (1984).

    Google Scholar 

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Authors
  1. A. É. Filippov
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Additional information

Donetsk Physicotechnical Institute, Ukrainian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 3, pp. 463–485, March, 1993.

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Filippov, A.É. Phenomenological approach to construction of attractors. Theor Math Phys 94, 325–338 (1993). https://doi.org/10.1007/BF01017265

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  • DOI: https://doi.org/10.1007/BF01017265

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