Open Access Research

Attractor bifurcation for FKPP type equation with periodic boundary condition

Qiang Zhang

Author Affiliations

College of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China

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

Boundary Value Problems 2012, 2012:41  doi:10.1186/1687-2770-2012-41

Published: 13 April 2012

Abstract

In this article, we make bifurcation analysis on the FKPP type equation under periodic boundary condition. And we show that the solutions bifurcate from the trivial solution u = 0 to an attractor ∑λ as parameter crosses certain critical value. Moreover, we prove that the attractor ∑λ consists of only one cycle of steady state solutions and is homeomorphic to S1. The analysis is based on a new theory of bifurcation, called attractor bifurcation, which was developed by Ma and Wang.

2000 Mathematics Subject Classification: 35B; 35Q; 37G; 37L.

Keywords:
FKPP type equation; periodic boundary condition; attractor bifurcation; center manifold