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Avtomatika i Telemekhanika, 2017, Issue 11, Pages 20–33 (Mi at14738)  
This article is cited in 11 scientific papers (total in 11 papers)

Nonlinear Systems

Local bifurcations in the periodic boundary value problem for the generalized Kuramoto–Sivashinsky equation

A. N. Kulikov, D. A. Kulikov

Demidov State University, Yaroslavl, Russia
Full-text PDF (624 kB) Citations (11)
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Abstract: For a version of the generalized Kuramoto–Sivashinsky equation with “violated” symmetry, the periodic boundary value problem was investigated. For the given dynamic distributed-parameter system, consideration was given to the issue of local bifurcations at replacing stability by spatially homogeneous equilibrium states. In particular, the bifurcation of the two-dimensional local attractor with all Lyapunov-unstable solutions on it was detected. Analysis of the bifurcation problem relies on the method of the integral manifolds and normal forms for the systems with infinitely dimensional space of the initial conditions.
Keywords: periodic boundary value problem, stability, bifurcation, normal forms, attractors, asymptotic formulas.
Presented by the member of Editorial Board: A. G. Kushner

Received: 31.03.2017
English version:
Automation and Remote Control, 2017, Volume 78, Issue 11, Pages 1955–1966
DOI: https://doi.org/10.1134/S0005117917110029
Bibliographic databases:
Document Type: Article
MSC: 35B32,35B41
Language: Russian
Citation: A. N. Kulikov, D. A. Kulikov, “Local bifurcations in the periodic boundary value problem for the generalized Kuramoto–Sivashinsky equation”, Avtomat. i Telemekh., 2017, no. 11, 20–33; Autom. Remote Control, 78:11 (2017), 1955–1966
Citation in format AMSBIB
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\paper Local bifurcations in the periodic boundary value problem for the generalized Kuramoto--Sivashinsky equation
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\issue 11
\pages 20--33
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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