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Hopf bifurcation from spike solutions for the weak coupling Gierer–Meinhardt system



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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L. Mei is supported by the National Natural Science Foundation of China (11771125, 11371117). J. Wei is partially supported by NSERC of Canada. D. Gomez is supported by NSERC of Canada.



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Hopf bifurcation from spike solutions for the weak coupling Gierer–Meinhardt system



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