Dynamical bifurcation of the one dimensional modified Swift-Hohenberg equation
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1241-1252
https://doi.org/10.4134/BKMS.2015.52.4.1241
Published online July 31, 2015
Yuncherl Choi
Kwangwoon University
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
MSC numbers : Primary 37G35, 35B32
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