Dynamic analysis of a soil organic matter and plant system with reaction-diffusion

Soil organic matter (SOM) is considered to be a driving factor in determining plant patterns, but few dynamic models include both plant and SOM. In this paper, we presented a plant-SOM model with reaction diffusion to understand how SOM affects dynamic changes of plant growth. We proposed the existence and uniqueness of the global positive solution of the model and then defined the basic reproduction number ℜ0: when ℜ0≤1, the plant-free equilibrium was globally asymptotically stable; when ℜ0>1, the solution to the system was uniformly persistent. We also confirmed the global attractivity of a unique positive equilibrium when all the parameters of this model are constant. Finally, we conducted numerical simulations to verify the effectiveness of the theoretical analysis.