Global analysis of a generalist predator–prey model with Holling type IV response function and harvesting

This study analyzes the global dynamics of a generalist predator–prey model with Holling type IV response function and harvesting of both populations. To ensure the well-posedness of the model, nonnegativity and uniform boundedness of the solutions are examined. The four equilibria of the system are determined and each equilibrium point investigated for local and global stability. We establish conditions for the nonexistence of periodic solutions along with persistence and permanence of the system. Further, bifurcation analysis is conducted on each equilibrium point to reveal the existence of transcritical and saddle–node bifurcations. We perform numerical simulations to validate the analytical results. The findings show that with high harvesting efforts exceeding the biotechnical productivity of each species, the populations can go extinct. In addition, partial survival of the species is possible depending on the level of harvesting effort in relation to the biotechnical productivity. Of particular interest is the ability of the predator to persist independently of prey, despite the presence of prey group defense and predator harvesting. This can be attributed to the availability of an alternative source of food for the predator. To maintain a sustainable ecosystem where both populations coexist in a stable equilibrium, the harvesting effort on each species should not exceed its biotechnical productivity. • Proposed a generalist predator–prey model with group defense and harvesting. • Explored uniform boundedness, local and global stability of the model. • Examined uniform persistence and permanence of the system. • Bifurcation analysis shows presence of transcritical and saddle–node bifurcations. • Numerical simulations indicate sustainable harvesting of populations feasible.