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About bifurcational parametric simplification. (English) Zbl 1347.34059

The authors introduce their concept of Bifurcational Parametric Simplification and explain its application to a chemical kinetic model, the Langmuir mechanism. In this model, the presence of a fast reaction rate leads to a singularly perturbed system of equations, which admits further simplifications. The authors investigate the existence and stability of steady states for varying system parameters.
The concept of Bifurcational Parametric Simplification seems to be some variant of the well-established notion of codimension for a bifurcation: The higher the degeneracy of some bifurcation, the more equations for the parameters are needed, thereby reducing the dimension of the parameter space.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
92E20 Classical flows, reactions, etc. in chemistry
34E15 Singular perturbations for ordinary differential equations

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References:

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