Bifurcation analysis of the Gierer–Meinhardt system with a saturation in the activator production

Shanshan Chen, Junping Shi, Junjie Wei
2013 Applicable Analysis  
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
more » ... aturation in different parameter regimes. S. Chen et al. (1.1) with κ = 0, (see [6] [7] [8] [9] [10] [11] [12] [13] ) and the Gierer-Meindardt system with saturation (1.1) with κ > 0, (see references [14] [15] [16] [17] ). There are also many results on the steady state solutions of other similar models, (see references [18] [19] [20] [21] [22] [23] ). In this paper, we analyse the Gierer-Meinhardt system with saturation in the following form (see [16, 24] ):
doi:10.1080/00036811.2013.817559 fatcat:pl3zouwn2nc5ngs7u46hjqnsgq