Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction–diffusion model

In this paper, we study the Hopf bifurcation phenomenon of a one-dimensional Schnakenberg reaction–diffusion model subject to the Neumann boundary condition. Our results reveal that both spatially homogeneous periodic solutions and spatially heterogeneous periodic solution exist. Moreover, we conclu...

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Published inNonlinear analysis: real world applications Vol. 13; no. 4; pp. 1961 - 1977
Main Authors Xu, Chuang, Wei, Junjie
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.08.2012
Subjects
Asymptotic properties
Boundary conditions
Hopf bifurcation
Mathematical models
Nonlinearity
Schnakenberg reaction–diffusion model
Spatially heterogeneous periodic solution
Spatially homogeneous periodic solution
Spatially homogeneous periodic solution
Schnakenberg reaction–diffusion model
Hopf bifurcation
Spatially heterogeneous periodic solution
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ISSN1468-1218
1878-5719
DOI10.1016/j.nonrwa.2012.01.001

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Summary:In this paper, we study the Hopf bifurcation phenomenon of a one-dimensional Schnakenberg reaction–diffusion model subject to the Neumann boundary condition. Our results reveal that both spatially homogeneous periodic solutions and spatially heterogeneous periodic solution exist. Moreover, we conclude that the spatially homogeneous periodic solutions are locally asymptotically stable and the spatially heterogeneous periodic solutions are unstable. In addition, we give specific examples to illustrate the phenomenon that coincides with our theoretical results.
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content type line 23
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2012.01.001