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unstable limit cycle

European Journal of Applied Mathematics (1)

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1 results

Hopf bifurcation from spike solutions for the weak coupling Gierer–Meinhardt system
Part of
- Physiological, cellular and medical topics
- Partial differential equations
DANIEL GOMEZ, LINFENG MEI, JUNCHENG WEI
Journal:

European Journal of Applied Mathematics / Volume 32 / Issue 1 / February 2021

Published online by Cambridge University Press:

17 March 2020, pp. 113-145
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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.