Abstract
The reaction-diffusion Gierer-Meinhardt system with a saturation in the activator production is considered. Stability of the unique positive constant steady state solution is analysed, and associated Hopf bifurcations and steady state bifurcations are obtained. A global bifurcation diagram of non-trivial periodic orbits and steady state solutions with respect to key system parameters is obtained, which improves the understanding of dynamics of Gierer-Meinhardt system with a saturation in different parameter regimes.
| Original language | English |
|---|---|
| Pages (from-to) | 1115-1134 |
| Number of pages | 20 |
| Journal | Applicable Analysis |
| Volume | 93 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2014 |
| Externally published | Yes |
Keywords
- Gierer-Meinhardt system with saturation
- Heterogeneous case
- Hopf bifurcation
- Steady state bifurcation
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