Hopf bifurcation from spike solutions for the weak coupling Gierer–Meinhardt system
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Bibliographic record
Abstract
The Hopf bifurcation from spike solutions for the classical Gierer–Meinhardt system in a onedimensional interval is considered. The existence of time-periodic solution near the Hopf bifurcation parameter for a boundary spike is rigorously proved by the classical Crandall–Rabinowitz theory. The criteria for the stability of the limit cycle are determined, and it is shown that the limit cycle is unstable .
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
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| Open science | 0.001 | 0.000 |
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