### Abstract

A plot of the bifurcation diagram for a two-component reaction-diffusion equation with no-flux boundary conditions reveals an intricate web of competing stable and unstable states. By studying the one-dimensional Sel'kov model, we show how a mixture of local, global and numerical analysis can make sense of several aspects of this complex picture. The local bifurcation analysis, via the power of singularity theory, gives us a framework to work in. We can then fill in the details with numerical calculations, with the global analytic results fixing the outline of the solution set. Throughout, we discuss to what extent our results can be applied to other models.

Original language | English |
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Pages (from-to) | 413-438 |

Number of pages | 26 |

Journal | Proceedings of the Royal Society of Edinburgh, Section A: Mathematics |

Volume | 125 |

Publication status | Published - 1995 |

### Cite this

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**ANALYSIS OF BIFURCATIONS IN REACTION-DIFFUSION SYSTEMS WITH NO-FLUX BOUNDARY-CONDITIONS - THE SELKOV MODEL.** / FURTER, J E ; EILBECK, J C .

Research output: Contribution to journal › Article

TY - JOUR

T1 - ANALYSIS OF BIFURCATIONS IN REACTION-DIFFUSION SYSTEMS WITH NO-FLUX BOUNDARY-CONDITIONS - THE SELKOV MODEL

AU - FURTER, J E

AU - EILBECK, J C

PY - 1995

Y1 - 1995

N2 - A plot of the bifurcation diagram for a two-component reaction-diffusion equation with no-flux boundary conditions reveals an intricate web of competing stable and unstable states. By studying the one-dimensional Sel'kov model, we show how a mixture of local, global and numerical analysis can make sense of several aspects of this complex picture. The local bifurcation analysis, via the power of singularity theory, gives us a framework to work in. We can then fill in the details with numerical calculations, with the global analytic results fixing the outline of the solution set. Throughout, we discuss to what extent our results can be applied to other models.

AB - A plot of the bifurcation diagram for a two-component reaction-diffusion equation with no-flux boundary conditions reveals an intricate web of competing stable and unstable states. By studying the one-dimensional Sel'kov model, we show how a mixture of local, global and numerical analysis can make sense of several aspects of this complex picture. The local bifurcation analysis, via the power of singularity theory, gives us a framework to work in. We can then fill in the details with numerical calculations, with the global analytic results fixing the outline of the solution set. Throughout, we discuss to what extent our results can be applied to other models.

M3 - Article

VL - 125

SP - 413

EP - 438

JO - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

SN - 0308-2105

ER -