The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior

In this paper, the conditions under which the occurrence of the local bifurcation (such as saddle-node (SN), transcritical (TC), and pitchfork (PT)) of all stable points of a food web model have been investigated. Fear and anti-predator responses involving the Holling-type IV and Growly-Martin functional responses have been found. It has been shown that there are transcritical and pitchfork bifurcations near H3, H4, and H6 as well as a saddle-node bifurcation close to the positive equilibrium point. In addition, there is a saddle-node bifurcation in close to the positive equilibrium point. These divergences have materialised into existence. In conclusion, To prove that the analytical results are correct, a numerical simulation of a set of parameters and starting conditions has been used.