Global Dynamics in a Beddington–DeAngelis Prey–Predator Model with Density Dependent Death Rate of Predator

The article aims to investigate a prey–predator model which includes density dependent death rate for predators and Beddington–DeAangelis type functional response. We observe the changes in the existence and stability of the equilibrium points and investigate the complete global dynamics of the model. A two-parametric bifurcation diagram has been described here which shows the effect of density dependent death rate parameter of predator. We have also examined all possible local and global bifurcations that the system could go through, namely transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, cusp bifurcation, Bogdanov–Takens bifurcation, Bautin bifurcation and homoclinic bifurcation.