Discrete-time predator-prey dynamics under human shielding: stability and bifurcation analysis

We propose and analyze a discrete-time predator-prey model incorporating a human-shield effect, whereby prey use human-dominated areas as partial refuges to reduce predation risk. Starting from a Rosenzweig-MacArthur-type framework, we introduce a nonnegative shielding intensity $h$ acting through two coupled mechanisms: it increases the effective prey carrying capacity $K\left(h\right)$ and weakens predation through the saturation parameter $\gamma \left(h\right)$ in a Holling type II functional response. We determine the equilibrium points, derive feasibility and local stability conditions, and identify the main bifurcation thresholds associated with predator invasion and coexistence dynamics. In particular, the model exhibits a transcritical bifurcation between the predator-free and coexistence equilibria, a period-doubling bifurcation, and a Neimark-Sacker bifurcation leading to oscillatory coexistence. Numerical simulations show that human shielding can promote prey persistence, shift the stability boundaries, and reduce the parameter region supporting predator-prey coexistence, eventually leading to predator exclusion for strong shielding intensity. A pathway-resolved analysis in the effective $(K,\gamma )$ -plane further separates the roles of prey support and predator deterrence. Finally, a state-feedback control strategy is shown to stabilize the coexistence equilibrium in regimes where the uncontrolled system displays large oscillations. Overall, the model provides a theoretical framework for understanding how human presence can reshape trophic regulation, persistence, and long-term population dynamics in anthropogenically modified landscapes.