Role of delay in plant growth dynamics: A two compartment mathematical model

Abstract

A mathematical model consisting of two compartments-shoot and root is used in this paper for the study of growth of an individual plant. The dynamics of plant growth is studied by division of plant in these two compartments where the associated state variables are structural dry weight and concentration of nutrients. The assumption is that the nutrient is taken up from the root compartment and the exogenic activities hinder the up taking of nutrients that are essential for the plants and adversely affect the nutrient use efficiency (utilization coefficients) resulting into root structural damage. This effect is studied by introducing the delay (time-lag) in utilization parameter. The inclusion of delay disturbed the Stability of the system and Hopf bifurcation occurred. Analytic results have been supported by numerical simulation using MATLAB.