Stability of stationary solutions to the shadow system for the activator-inhibitor system proposed by Gierer and Meinhardt is considered in higher dimensional domains. It is shown that a stationary solution with minimal "energy" is stable in a weak sense if the inhibitor reacts sufficiently fast, while it is unstable whenever the reaction of the inhibitor is slow. Moreover, the loss of stability results in a Hopf bifurcation.
|Original language||English (US)|
|Number of pages||14|
|Journal||Japan Journal of Industrial and Applied Mathematics|
|State||Published - Jun 2001|
- Hopf bifurcation
- Reaction-diffusion system
- Shadow system