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Avtomatika i Telemekhanika, 2021, Issue 2, Pages 94–110
DOI: https://doi.org/10.31857/S0005231021020069 (Mi at15669) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Nonlinear Systems

Invariant manifolds of a weakly dissipative version of the nonlocal Ginzburg–Landau equation

A. N. Kulikov, D. A. Kulikov

Demidov Yaroslavl State University, Yaroslavl, 150003 Russia
Full-text PDF (251 kB) Citations (7)
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DOI: https://doi.org/10.31857/S0005231021020069
Abstract: We consider a periodic boundary value problem for a nonlocal Ginzburg–Landau equation in its weakly dissipative version. The existence, stability, and local bifurcations of one-mode periodic solutions are studied. It is shown that in a neighborhood of one-mode periodic solutions there may exist a three-dimensional local attractor filled with spatially inhomogeneous time-periodic solutions. Asymptotic formulas for these solutions are obtained. The results are based on using and developing methods of the theory of infinite-dimensional dynamical systems. In a special version of the partial integro-differential equation considered, we study the existence of a global attractor. Solution in the form of series are obtained for this version of the nonlinear boundary value problem.
Keywords: partial integro-differential equation, local attractors, global attractor, stability, bifurcation.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00672
This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00672.
Presented by the member of Editorial Board: A. G. Kushner

Received: 04.03.2020
Revised: 05.06.2020
Accepted: 09.07.2020
English version:
Automation and Remote Control, 2021, Volume 82, Issue 2, Pages 264–277
DOI: https://doi.org/10.1134/S0005117921020065
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. N. Kulikov, D. A. Kulikov, “Invariant manifolds of a weakly dissipative version of the nonlocal Ginzburg–Landau equation”, Avtomat. i Telemekh., 2021, no. 2, 94–110; Autom. Remote Control, 82:2 (2021), 264–277
Citation in format AMSBIB
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\paper Invariant manifolds of a weakly dissipative version of the nonlocal Ginzburg--Landau equation
\jour Avtomat. i Telemekh.
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\pages 94--110
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\pages 264--277
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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