NUMERICAL ANALYSIS OF A PREY-PREDATOR MODEL WITH CROWLEY MARTIN RESPONSE FUNCTION AND MICHALES-MENTEN TYPE HARVESTING

摘要

The present study deals with the dynamical response of a predator-prey model in which the prey has been subjected to harvesting. The proposed model considers a Crowley-Martin response function which is subjected to Michaelis-Menten type prey harvesting. It is first shown that the system is bounded and the conditions of existence and stability of the equilibria of the proposed model have been furnished. Next the presence of Hopf bifurcation and limit cycles have been shown to explain the transition of the model from a stable to an unstable one. It is seen that harvesting effort has a remarkable effect on the dynamics of the system and can make the system undergo unstability by reaching beyond a critical value. The model can be useful to study the ecological dynamics of the prey-predtor system and to help create harvested environments where the prey-predator species can thrive suitably.