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Asymptotic behavior of solutions of Lorenz-like systems: Analytical results and computer error structures

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Abstract

For Lorenz-like systems with volume contractions, analytical criteria for the global stability and instability of stationary sets are obtained. Numerical experiments for the study of the qualitative behavior of trajectories of Lorenz-like systems are described and analyzed. It is shown that their interpretation can lead to incorrect conclusions unless an additional verification oriented to the analytical results is performed.

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Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    G. A. Leonov & R. N. Mokaev

  2. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russia

    G. A. Leonov, B. R. Andrievskiy & R. N. Mokaev

  3. St. Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University), St. Petersburg, 197101, Russia

    B. R. Andrievskiy

Authors
  1. G. A. Leonov
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  2. B. R. Andrievskiy
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  3. R. N. Mokaev
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Correspondence to G. A. Leonov.

Additional information

Original Russian Text © G.A. Leonov, B.R. Andrievskiy, R.N. Mokaev, 2017, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2017, Vol. 62, No. 1, pp. 25–37.

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Leonov, G.A., Andrievskiy, B.R. & Mokaev, R.N. Asymptotic behavior of solutions of Lorenz-like systems: Analytical results and computer error structures. Vestnik St.Petersb. Univ.Math. 50, 15–23 (2017). https://doi.org/10.3103/S1063454117010071

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  • DOI: https://doi.org/10.3103/S1063454117010071

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