  Bifurcation of the local Gierer-Meinhardt model is analyzed in this paper. It
is found that the degenerate Bogdanov-Takens bifurcation of codimension 3
happens in the model, except that teh saddle-node bifurcation and the Hopf
bifurcation. That was not reported in the existing results about this model.
The existence of equilibria, their stability, the bifurcation and the induced
complicated and interesting dynamics are explored in detail, by using the
stability analysis, the normal form method and bifurcation theory. Numerical
results are also presented to validate theoretical results.
