Bifurcation analysis of a predator-prey system with density dependent disease recovery

The center manifold is an invariant that plays a crucial role in the bifurcation analysis of dynamical systems. existence theorem assures local submanifold state space system around non-hyperbolic equilibrium point. Center theory essential reduction different scenarios to their normal forms. Our study focuses on predator-prey interactive with density-dependent growth predators subject contagious disease. disease assumed be horizontally transmitted, and rate recovery infected predator density-dependent. At trivial (zero) equilibrium, calculated whose behaviour similar original system. Further, using manifolds, form Hopf point determined fromwhich criticality can deduced. Finally, numerical simulations are performed biologically plausible parameters substantiate analytical findings. Using continuation methods we detect Generalized Zero-Hopf points. We discuss coefficients, compute two-parameter unfoldings relate these results mathematical codimension two bifurcations.