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http://dx.doi.org/10.4134/BKMS.2015.52.4.1241

DYNAMICAL BIFURCATION OF THE ONE DIMENSIONAL MODIFIED SWIFT-HOHENBERG EQUATION  

CHOI, YUNCHERL (DIVISION OF GENERAL EDUCATION KWANGWOON UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.4, 2015 , pp. 1241-1252 More about this Journal
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;
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