Analysis of bifurcations in reaction-diffusion systems with no-flux boundary conditions: The Sel’kov model. (English) Zbl 0830.35011
As a special case of a two-component reaction-diffusion equation with no- flux boundary condition the one-dimensional Sel’kov model is studied. It is shown how the boundary conditions determine the symmetry of the problem, leading to pitchfork bifurcations of the primary branches. The bifurcations from the steady state solutions at simple and double bifurcation points are calculated analytically. Using analytical and numerical methods a two-dimensional parameter plane is divided into regions of similar bifurcation diagrams and the organizing centers are located. Global estimates, numerical results from a pathfollowing procedure and asymptotic estimates for limiting values of the diffusion coefficients contribute to a better understanding of the complicated structure of the bifurcation set.
Reviewer: A.Steindl (Wien)
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35K57 | Reaction-diffusion equations |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
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