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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.

Mathematical modeling of rhizosphere microbial degradation with impulsive diffusion on nutrient