Open Access Research

Attractor bifurcation for the extended Fisher-Kolmogorov equation with periodic boundary condition

Qiang Zhang1* and Hong Luo2

Author Affiliations

1 College of Computer Science, Civil Aviation Flight University of China, Guanghan, Sichuan, 618307, P.R. China

2 College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, P.R. China

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Boundary Value Problems 2013, 2013:169  doi:10.1186/1687-2770-2013-169

Published: 19 July 2013

Abstract

In this paper, we study the bifurcation and stability of solutions of the extended Fisher-Kolmogorov equation with periodic boundary condition. We prove that the system bifurcates from the trivial solution to an attractor as parameter crosses certain critical value. The topological structure of the attractor is also investigated.

MSC: 35B32, 35K35, 37G35.

Keywords:
extended Fisher-Kolmogorov equation; periodic boundary condition; attractor bifurcation; center manifold