A Study of Effect of Pollution on the Dynamics of Predator Prey Interactions

Abstract

In this work, the effect of pollution on four different predator-prey systems has been studied. For the first three systems, autonomous differential equation models have been proposed. The first model consists of one prey and one predator; the second is for two competitive prey and one predator, and the third deals with two competitive predators and one prey. It has been shown that these models satisfy the criterion for non-negativity and boundedness of solutions. newlineFurther, the criteria for the existence of equilibria and their stability, both local and global, have been derived. In each model, the possibility of the occurrence of Hopf-Bifurcation has also been analyzed. The conditions for the uniform persistence of these systems in a polluted environment have also been discussed. newlineThe results are justified with the help of numerical examples by taking appropriate functions satisfying assumptions. newlineThe fourth model represents a system of one prey and one predator with a discrete delay in prey growth rate. In this model, mathematical criteria for the boundedness of solutions and asymptotic stability of the equilibrium points have been derived. newline newline newline