Effect of an amount of extra food on the dynamics of a food -web model with modified Holling type II functional response

This paper deals with studding the effect of an amount of additional food supplies on the dynamic interaction of three species food-web, the species are, prey, intermediate predators and top predators. The top predator species predate both prey species and intermediate predator species according to extended Holling type II functional response for two prey species. Firstly it is proved that the model solutions are bounded under certain condition. All biological possible steady states are explored, and their local stability is analyzed based on the sample parameters. Critical values that make the occurrence of Hopf-bifurcation of the model near intermediate predators-free and top predator-free steady states are determined. Finally, with the help of MATLAB, it is performed numerical simulations to support the evidence of the analytical results regarding to stability and Hopf- bifurcation , Further it is observed that when the amount of extra food increases, the dynamics of the model may induced a transition from the a stability situation to the state where populations oscillate periodically.