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Avtomatika i Telemekhanika, 2017, Issue 11, Pages 20–33
(Mi at14738)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/at14738 https://www.mathnet.ru/eng/at/y2017/i11/p20
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Abstract page: | 186 | Full-text PDF : | 30 | References: | 40 | First page: | 23 |
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