Butterfly catastrophe for fronts in a three-component reaction-diffusion system. (English) Zbl 1325.35088
The subject of the paper is the analysis of bifurcations of solutions for propagating fronts in a three-component one-dimensional reaction-diffusion model of the FitzHugh-Nagumo type, where single- and multiple-front patterns are basic dynamical states. The application of a combination of various analytical methods, such as singular perturbation theory, center-manifold reduction, and Evans function, reveals a rather complex picture of bifurcations. These results suggest an explanation to numerically observed dynamical regimes in the form of accelerating and oscillating fronts. The most essential peculiarity of the analysis is that it focuses on the case when the essential spectrum of perturbations around the underlying front solution is asymptotically close to the imaginary axis.
Reviewer: Boris A. Malomed (Tel Aviv)
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35B36 | Pattern formations in context of PDEs |
| 35B25 | Singular perturbations in context of PDEs |
| 35B32 | Bifurcations in context of PDEs |
Keywords:
FitzHugh-Nagumo model; singular perturbation theory; center-manifold reduction; Evans functionReferences:
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