Modeling and Analysis of Delay on Plant Population Growth Induced by Toxic Metal

Abstract

It is an ecological phenomenon that nutrient pool and plant population density are adversely affected by the presence of excessive toxic metal. This dynamic is mathematically depicted by the model proposed in this study. It is shown that as the input rate of toxic metal increase, the nutrient pool concentration and plant population density decreases. Hopf bifurcation is studied by introducing delay parameter in the term involving nutrient utilization. Sensitivity analysis with respect to parameters is done. Model is verified by taking those values of damage rate due to toxic metal (assumed to be Arsenic) which are available in already existing data for growth of Triticum aestivum L and Brassica napus under the effect of amplified concentrations of Arsenic in soil (Liu et al 2012). Simulation is done using MATLAB.