Stability analysis on steady-state bifurcation for arbitrary order autocatalytic reaction model. (English) Zbl 1423.35028
Summary: This paper deals with an autocatalytic reaction-diffusion model with arbitrary order functional response subject to no-flux boundary conditions. We mainly discuss the stability of the steady-state bifurcation which emanates from the unique positive constant equilibrium. On the stability of the bifurcation solution, the conventional way is to consider the sign of the first derivative of a certain function. However, sometimes, the first derivative may be equal to zero. This leads to the uncertainty of the stability. In such case, it needs to break through the common idea. We present an approach which determines the stability of the bifurcation solution.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35K57 | Reaction-diffusion equations |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K58 | Semilinear parabolic equations |
| 35B35 | Stability in context of PDEs |
| 92E20 | Classical flows, reactions, etc. in chemistry |
Keywords:
no-flux boundary conditionsReferences:
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