Bifurcation Analysis on the Dynamics of a Genralist Predator-Prey System

In this paper a generalist predator prey system is modeled as a two dimensional coupled differential system. We identified three vital parameters stands for the maximum uptake rate of the generalist predator, stands for half saturation value and such that is the conversion efficiency of the generalist predator where is the intrinsic growth rate of the predator. Using these parameters a novel way to divide the parameter space based on the number of interior equilibrium solutions admitted by the system has been presented. We investigate the considered model is reach in dynamics and identified various bifurcations that are experienced by the considered system from the parameter space. These are Saddle-Node bifurcation, Trans-Critical bifurcation and pitchfork bifurcation. In this study we offer mathematical proof for the incidence of these bifurcations that take place in the considered dynamical system as the parameters move between the regions presented in the parameter space.