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DYNAMICAL BIFURCATION OF THE ONE DIMENSIONAL MODIFIED SWIFT-HOHENBERG EQUATION
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 Title & Authors
DYNAMICAL BIFURCATION OF THE ONE DIMENSIONAL MODIFIED SWIFT-HOHENBERG EQUATION
CHOI, YUNCHERL;
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 Abstract
In this paper, we study the dynamical bifurcation of the modified Swift-Hohenberg equation on a periodic interval as the system control parameter crosses through a critical number. This critical number depends on the period. We show that there happens the pitchfork bifurcation under the spatially even periodic condition. We also prove that in the general periodic condition the equation bifurcates to an attractor which is homeomorphic to a circle and consists of steady states solutions.
 Keywords
modified Swift-Hohenberg equation;dynamic bifurcation;center manifold function;
 Language
English
 Cited by
1.
Bifurcation and final patterns of a modified Swift-Hohenberg equation, Discrete and Continuous Dynamical Systems - Series B, 2017, 22, 7, 2543  crossref(new windwow)
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