• MODELING THE EFFECT OF HARVESTING OF THE VEGETATION BIOMASS AND GRAZER POPULATION ON PREDATOR POPULATION WITH HABITAT COMPLEXITY

Abstract

In this paper, a nonlinear mathematical model is proposed and analyzed to see the effect of harvesting of vegetation biomass and grazer population on the predator population. The model is formulated as a food chain model by considering the hyperbolic interaction processes. It is assumed that the dynamics of vegetation biomass follows regrowth equation. We also study the effect of the degree of habitat complexity and gestation delay on the stability of a food chain model. It is observed that there are stability switches, and Hopf bifurcation occurs when the delay crosses some critical value. It is observed that the quantitative level of abundance of system populations depends crucially on the delay parameter if the gestation period exceeds some critical value. However, the fluctuations in the population levels can be controlled completely by increasing the degree of habitat complexity.