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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 8, Pages 1415–1422 (Mi zvmmf427)  

This article is cited in 3 scientific papers (total in 3 papers)

Numerical stabilization of the Lorenz system by a small external perturbation

A. I. Noarov

Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119992, Russia

Abstract: The Lorenz system perturbed by noise and its invariant measure whose density obeys the stationary Fokker–Planck equation are analyzed numerically. A linear functional of the invariant measure is considered, and its variation caused by a variation in the right-hand side of the Lorenz system is calculated. A small (in modulus) external perturbation is calculated under which the strange attractor of the Lorenz system degenerates into a stable fixed point.

Key words: Lorenz system, Fokker–Planck equation, stochastic differential equations, chaotic dynamics.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:8, 1341–1348

Bibliographic databases:

UDC: 519.62
Received: 05.07.2005

Citation: A. I. Noarov, “Numerical stabilization of the Lorenz system by a small external perturbation”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1415–1422; Comput. Math. Math. Phys., 46:8 (2006), 1341–1348

Citation in format AMSBIB
\Bibitem{Noa06}
\by A.~I.~Noarov
\paper Numerical stabilization of the Lorenz system by a~small external perturbation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1415--1422
\mathnet{http://mi.mathnet.ru/zvmmf427}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287359}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1341--1348
\crossref{https://doi.org/10.1134/S0965542506080069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748308832}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Noarov, “Numerical optimization of certain dynamical stochastic systems”, Comput. Math. Math. Phys., 47:7 (2007), 1129–1136  mathnet  crossref  mathscinet
    2. A. I. Noarov, “On the substantiation of a projection method for the stationary Fokker–Planck equation”, Comput. Math. Math. Phys., 51:4 (2011), 602–608  mathnet  crossref  mathscinet  isi
    3. A. I. Noarov, “Numerical solution to a system of differential equations for probability measures”, Comput. Math. Math. Phys., 58:9 (2018), 1404–1410  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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