Bifurcation analysis of a three species discrete-time predator-prey model

We explore local dynamics at fixed points, existence of periodic points and bifurcation analysis of a three species discrete predator-prey model. More precisely, it is explored that model has trivial fixed point, five boundary fixed points and the interior fixed point under definite parametric conditions. We have also constructed the linearized system for the model under consideration. Then we have investigated local stability analysis with topological classifications at each fixed points by linear stability theory. Further existence of periodic points and bifurcation analysis at each fixed points are also demonstrated. The extensive numerical simulations are provided to demonstrate theoretical results.