Dynamics of a depletion-type Gierer-Meinhardt model with Langmuir-Hinshelwood reaction scheme

<p style='text-indent:20px;'>A depletion-type reaction-diffusion Gierer-Meinhardt model with Langmuir-Hinshelwood reaction scheme and the homogeneous Neumann boundary conditions is introduced investigated in this paper. Firstly, boundedness of positive solution parabolic system given, constant steady state solutions are exhibited by Shengjin formulas. Through rigorous theoretical analysis, stability corresponding explored. Next, a priori estimates, properties nonconstant states, non-existence existence for elliptic some estimates Leray-Schauder degree theory, respectively. Then, established Hopf bifurcation presented, It showed that temporal spatial structures will appear model. Theoretical results confirmed complemented numerical simulations.</p>