Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model (Q1884256)
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scientific article; zbMATH DE number 2110796
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model |
scientific article; zbMATH DE number 2110796 |
Statements
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model (English)
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27 October 2004
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The main result of this paper is the determination of the existence and stability properties of interior spike solutions in a dumbbell-shaped domain for different asymptotic regimes of \(D(\varepsilon)\) as \(\varepsilon\) decreases to zero. The pitchfork bifurcation behavior that occurs in the range \(O(\varepsilon^2)\ll D\ll O(-\log\varepsilon)\) is analyzed in more detail numerically.
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Green's function
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pattern formation
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pitchfork bifurcation
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