Hopf bifurcation and steady-state bifurcation for an autocatalysis reaction–diffusion model

This paper is concerned with an autocatalysis model subject to no-flux boundary conditions. The existence of Hopf bifurcation are firstly obtained. Then by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous and inhomoge...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 391; no. 1; pp. 265 - 277
Main Authors Guo, Gaihui, Li, Bingfang, Wei, Meihua, Wu, Jianhua
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2012
Subjects
Diffusion
Hopf bifurcation
Steady-state bifurcation
Steady-state bifurcation
Hopf bifurcation
Diffusion
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ISSN0022-247X
1096-0813
DOI10.1016/j.jmaa.2012.02.012

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Summary:This paper is concerned with an autocatalysis model subject to no-flux boundary conditions. The existence of Hopf bifurcation are firstly obtained. Then by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous and inhomogeneous periodic solutions are established. On the other hand, the steady-state bifurcations from simple and double eigenvalues are intensively studied. The techniques of space decomposition and implicit function theorem are adopted to deal with the case of double eigenvalues. Finally, some numerical simulations are shown to verify the analytical results.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.02.012