Qualitative analysis for a biological depletion model

Abstract In this paper, we deal with a depletion model which is constructed by an activator and a substrate in a bounded domain. A better understanding of the asymptotic stability of constant solutions is obtained for such a general depletion model. The difficulty lies in how to clarify the number and the region of constant solutions. Next, we analyze the steady-state bifurcation from constant solutions. Finally, some numerical simulations are done to complement analytical results, and steady spike solutions are observed for proper parameters.