Stability Analysis of a Discrete Time Model on Plant-Soil Interactions

Abstract

In this paper, a nonlinear mathematical model on plant soil interactions is proposed and analyzed. We consider the variables namely, density of the plant species, nutrient concentration in the soil and in the plant for metabolic activity. We consider that the growth rate of the plant species is dependent on the density of the nutrient concentration in the plant. The relationship between the concentration and the rate of uptake is often described quantitatively by Michaelis?Menten kinetics. We discretize the model by applying Backward Euler method and analyse the stability of the model both locally and globally. We analyse the nutrient concentration in Tomato plant and provide numerical simulations for the dynamical behaviour of plant soil interactions for each nutrient. The numerical simulations are provided using MATLAB

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