Mathematical modeling of rhizosphere microbial degradation with impulsive diffusion on nutrient.

In this paper, a new mathematical modeling of rhizosphere microbial degradation with impulsive diffusion is proposed. By using the Floquet theorem, we find the rhizosphere microbe-eradication periodic solution is globally asymptotically stable if some conditions are satisfied. At the same time we also obtain the permanent conditions of the nutrients and rhizosphere microbe. Finally, a system of equations is solved by using a numerical simulation to justify our results. [ABSTRACT FROM AUTHOR]