Abstract
This paper deals with an autocatalytic reaction–diffusion model with arbitrary order functional response subject to no-flux boundary conditions. We mainly discuss the stability of the steady-state bifurcation which emanates from the unique positive constant equilibrium. On the stability of the bifurcation solution, the conventional way is to consider the sign of the first derivative of a certain function. However, sometimes, the first derivative may be equal to zero. This leads to the uncertainty of the stability. In such case, it needs to break through the common idea. We present an approach which determines the stability of the bifurcation solution.
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