Spatiotemporal patterns in a reaction–diffusion model with the Degn–Harrison reaction scheme

Spatial and temporal patterns generated in ecological and chemical systems have become a central object of research in recent decades. In this work, we are concerned with a reaction–diffusion model with the Degn–Harrison reaction scheme, which accounts for the qualitative feature of the respiratory process in a Klebsiella aerogenes bacterial culture. We study the global stability of the constant steady state, existence and nonexistence of nonconstant steady states as well as the Hopf and steady state bifurcations. In particular, our results show the existence of Turing patterns and inhomogeneous periodic oscillatory patterns while the system parameters are all spatially homogeneous. These results also exhibit the critical role of the system parameters in leading to the formation of spatiotemporal patterns.