Dynamics of cannibalism in the predator in a prey refuge functional response dependent predator-prey model

The mathematical model for predator-prey interactions discussed in this article includes cannibalism in the predator. Cannibalism is pervasive in natural individuals which reflects the potential to modify their functional relationship for interacting with resources. We have considered here prey refuge, which depends on the contacts between both the species. Predator consumes the prey according to Holling type II functional response. Feasibility as well as stability of the points of equilibria and the existence of Hopf bifurcation along with its direction at interior equilibrium have been duly accomplished and in this regard suitable graphical representation with proper discussions are executed to substantiate the system under consideration.