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Dynamical chaos in two-dimensional nonlinear nonautonomous systems of ordinary differential equations

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References

  1. Hirsch, M.W., Smale, S., and Devaney, R.L., Differential Equations, Dynamical Systems, and an Introduction to Chaos, Amsterdam: Elsevier, 2004.

    MATH  Google Scholar 

  2. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, New York: Springer, 1983.

    MATH  Google Scholar 

  3. Malinetskii, G.G. and Potapov, A.B., Sovremennye problemy nelineinoi dinamiki (Modern Problems of Nonlinear Dynamics), Moscow: Editorial URSS, 2002.

    Google Scholar 

  4. Loskutov, A.Yu. and Mikhailov, A.S., Vvedenie v sinergetiku (Introduction to Sinergetics), Moscow: Nauka, 1990.

    Google Scholar 

  5. Berger, P., Pomeau, Y., and Vidal, C., Order Within Chaos, Paris: Hermann, 1984. Translated under the title Poryadok v khaose, Moscow: Merkurii-Press, 2000.

    Google Scholar 

  6. Chen, G. and Dong, X., From Chaos to Order: Perspectives, Methodologies and Applications, Singapore: World Scientific, 1998.

    Google Scholar 

  7. Palis, J. and de Melo, W., Geometric Properties of Dynamical Systems. An Introduction, New York: Springer, 1982. Translated under the title Geometricheskaya teoriya dinamicheskikh sistem: vvedenie, Moscow: Mir, 1986.

    Google Scholar 

  8. Schuster, H.G., Deterministic Chaos, Weinheim: VCH, 1989. Translated under the title Determinirovannyi khaos: vvedenie, Moscow: Mir, 1989.

    MATH  Google Scholar 

  9. Anishchenko, V.S., Vadivasova, T.E., and Astakhov, V.V., Nelineinaya dinamika khaoticheskikh i stokhasticheskikh sistem (Nonlinear Dynamics of Chaotic and Stochastic Systems), Saratov: Izdat. Saratov. Univ., 1999.

    Google Scholar 

  10. Tucker, W., Found Comput. Math., 2002, vol. 2, p. 53.

    MathSciNet  Google Scholar 

  11. Feigenbaum, M.J., J. Statist. Phys., 1978, vol. 19, pp. 25–52.

    Article  MathSciNet  Google Scholar 

  12. Ruelle, D. and Takens, F., Commun. Math. Phys., 1971, vol. 20, no. 3, pp. 167–192.

    Article  MathSciNet  Google Scholar 

  13. Manneville, P. and Pomeau, Y., Physica, 1980, vol. 1D, p. 219.

    MathSciNet  Google Scholar 

  14. Sharkovskii, A.N., Ukrain. Mat. Zh., 1964, vol. 26, no. 1, pp. 61–71.

    MathSciNet  Google Scholar 

  15. Magnitskii, N.A. and Sidorov, S.V., Differ. Uravn., 2001, vol. 37, no. 11, pp. 1494–1506.

    MathSciNet  Google Scholar 

  16. Magnitskii, N.A. and Sidorov, S.V., Differ. Uravn., 2002, vol. 38, no. 12, pp. 1606–1610.

    MathSciNet  Google Scholar 

  17. Magnitskii, N.A., in Nelineinaya dinamika i upravlenie (Nonlinear Dynamics and Control), Emel’yanov, S.V. and Korovin, S.K., Eds., Moscow, 2004, issue 4, pp. 37–58.

  18. Magnitskii, N.A. and Sidorov, S.V., Novye metody khaoticheskoi dinamiki (New Methods of Chaotic Dynamics), Moscow: URSS, 2004.

    Google Scholar 

  19. Magnitskii, N.A. and Sidorov, S.V., Differ. Uravn., 2004, vol. 40, no. 11, pp. 1500–1514.

    MathSciNet  Google Scholar 

  20. Magnitskii, N.A., Proc. of ENOC-2005 Int. Conf., Eindhoven, 2005, pp. 1285–1294.

  21. Magnitskii, N.A. and Sidorov, S.V., Differ. Uravn., 2005, vol. 41, no. 11, pp. 1550–1558.

    MathSciNet  Google Scholar 

  22. Goryachenko, V.D., Elementary teorii kolebanii (Elements of Oscillation Theory), Moscow: Vysshaya Shkola, 2001.

    Google Scholar 

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Authors and Affiliations

  1. Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    N. A. Magnitskii & S. V. Sidorov

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  1. N. A. Magnitskii
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  2. S. V. Sidorov
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Original Russian Text © N.A. Magnitskii, S.V. Sidorov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 11, pp. 1507–1514.

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Magnitskii, N.A., Sidorov, S.V. Dynamical chaos in two-dimensional nonlinear nonautonomous systems of ordinary differential equations. Diff Equat 42, 1579–1586 (2006). https://doi.org/10.1134/S0012266106110073

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  • DOI: https://doi.org/10.1134/S0012266106110073

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