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

TY - JOUR

T1 - Local and global behaviour of steady-state solutions of the Sel'kov model

AU - Davidson, F. A.

AU - Rynne, B. P.

PY - 1996/4

Y1 - 1996/4

N2 - 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.

AB - 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.

U2 - 10.1093/imamat/56.2.145

DO - 10.1093/imamat/56.2.145

M3 - Article

SN - 0272-4960

VL - 56

SP - 145

EP - 155

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 2

ER -