Spatiotemporal pattern formation of a diffusive bimolecular model with autocatalysis and saturation law

Abstract

In this paper, a reaction–diffusion bimolecular model with autocatalysis and saturation law is investigated. Firstly, we provide some conditions for the stability/Turing instability of the constant positive solution. Then we mainly consider Hopf bifurcations and steady state bifurcations which bifurcate from the unique constant positive solution of the system. Our results suggest the existence of spatially non-homogeneous periodic orbit and non-constant positive steady state solutions, which implies the possibility of rich spatiotemporal patterns in this diffusive bimolecular model. Numerical examples are presented to support our theoretical analysis. Furthermore, non-existence of non-constant steady state is investigated in terms of parameters.