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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 365436, 11 pages
http://dx.doi.org/10.1155/2013/365436
Research Article

Attractor Bifurcation for Extended Fisher-Kolmogorov Equation

1Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, China
2School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 7 July 2013; Accepted 7 August 2013

Academic Editor: Feliz Minhós

Copyright © 2013 Honglian You et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the asymptotic stability and attractor bifurcation of the extended Fisher-Kolmogorov equation on the one-dimensional domain with Dirichlet or periodic boundary conditions. The novelty of this paper is that, based on a new method called attractor bifurcation, we investigate the existence of an attractor bifurcated from the trivial solution and give an explicit description of the bifurcated attractor. Moreover, the stability of the bifurcated branches is discussed.