Local and global behaviour of steady-state solutions of the Sel'kov model

F. A. Davidson, B. P. Rynne

Research output: Contribution to journalArticle

Abstract

In this paper we discuss steady-state solutions of the system of reaction-diffusion equations known as the Sel'kov model. This model has been the subject of much discussion; in particular, analytical and numerical results have been discussed by Lopez-Gomez et al (1992, IMA J. Num. Anal. 12, 405-28). We show that a simple analysis of the bifurcation function associated with the system can explain many of the numerical observations, such as the formation and development of loops of nontrivial solutions, in a simpler and more complete manner than the analysis of Lopez-Gomez et al. This allows for a clearer understanding of the qualitative behaviour of the set of nontrivial solutions and hence of the bifurcation diagram.

Original languageEnglish
Pages (from-to)145-155
Number of pages11
JournalIMA Journal of Applied Mathematics
Volume56
Issue number2
DOIs
Publication statusPublished - Apr 1996

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Steady-state Solution
Nontrivial Solution
Qualitative Behavior
Bifurcation Diagram
Reaction-diffusion Equations
Bifurcation
Numerical Results
Model
Observation

Cite this

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Local and global behaviour of steady-state solutions of the Sel'kov model. / Davidson, F. A.; Rynne, B. P.

In: IMA Journal of Applied Mathematics, Vol. 56, No. 2, 04.1996, p. 145-155.

Research output: Contribution to journalArticle

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