Attractor bifurcation for the extended Fisher-Kolmogorov equation with periodic boundary condition
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
Boundary Value Problems 2013, 2013:169 doi:10.1186/1687-2770-2013-169Published: 19 July 2013
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.