Dynamics of Forest Biomass and Soil Nutrients Effected by Delay Parameter

Abstract

This paper shows how the exploitation of natural forest by human activities can lead to drastic
variations in forest biomass. A model is framed which depicts the dynamics of forest biomass and soil
nutrient. This model shows how the mortality can rise if the acidity in the soil exceeds a particular
threshold value. This threshold value is represented by delay parameter. In fact, the model reveals
how the inflow of nutrient can get effected by exogenic activities and how the system exhibits
complex behaviour. Two state variables considered are: nutrient pool and forest biomass.
Boundedness, positivity, equilibrium points and stability analysis of equilibrium point is performed.
Time delay is taken as the bifurcating parameter which disturbs the stability of feasible interior
equilibrium and leads to Hopf bifurcation. Numerical simulation supports the theoretical results