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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 7, Pages 1237–1250 (Mi zvmmf628)  

This article is cited in 5 scientific papers (total in 5 papers)

The dynamical system response to a small variation of the right-hand side and finite-dimensional analogues of the Fokker–Planck equation

A. I. Noarov

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

Abstract: The change of a steady-state solution to the Fokker–Planck equation in response to small variations of the right-hand side (vector field) of the corresponding unperturbed system is investigated. Certain functionals of a steady-state solution and their dependence on the right-hand side of the unperturbed system are considered. This dependence is linearized, and an algorithm for computing its linear part is constructed. The applicability of the developed method to the control of dynamical systems is discussed.

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

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:7, 1195–1208

Bibliographic databases:
UDC: 519.634
Received: 01.04.2003
Revised: 03.02.2005

Citation: A. I. Noarov, “The dynamical system response to a small variation of the right-hand side and finite-dimensional analogues of the Fokker–Planck equation”, Zh. Vychisl. Mat. Mat. Fiz., 45:7 (2005), 1237–1250; Comput. Math. Math. Phys., 45:7 (2005), 1195–1208

Citation in format AMSBIB
\Bibitem{Noa05}
\by A.~I.~Noarov
\paper The dynamical system response to a small variation of the right-hand side and finite-dimensional analogues of the Fokker--Planck equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 7
\pages 1237--1250
\mathnet{http://mi.mathnet.ru/zvmmf628}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2188415}
\zmath{https://zbmath.org/?q=an:1074.82024}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 7
\pages 1195--1208


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Noarov, “Numerical stabilization of the Lorenz system by a small external perturbation”, Comput. Math. Math. Phys., 46:8 (2006), 1341–1348  mathnet  crossref  mathscinet
    2. A. I. Noarov, “Numerical optimization of certain dynamical stochastic systems”, Comput. Math. Math. Phys., 47:7 (2007), 1129–1136  mathnet  crossref  mathscinet
    3. 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
    4. 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
    5. Noarov A.I., “Efficient Projection Method For a System of Differential Equations of Fokker-Planck Type”, Russ. J. Numer. Anal. Math. Model, 34:3 (2019), 133–142  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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