Multiple bifurcations generated by mode interactions in a reaction-diffusion problen

• Main Authors: Y. S. Liao, 廖益賢
• Other Authors: C.-S.Chien
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/78423736989471529928

碩士 === 國立中興大學 === 應用數學系 === 87 === We study multiple bifurcations in a system of reaction-diffusion equations defined on a unit square with Robin boundary conditions. First we investigate linear stabilities of the system at the uniform steady state solution. Then we discuss how muliple bifurcations can be generted by mode interactions of the system, and how these multiple bifurcations can be preserved in the associated discrete system. A continuation-unsymmetric Lanczos algorthm is described to trace discrete solution curves. Numerical experiments on the Brusselator equations are reported.