Influence of predator mutual interference and prey refuge on Lotka–Volterra predator–prey dynamics

• A predator–prey model with predator mutual interference and prey refuge is presented.
• The interior equilibrium is globally stable for arbitrary prey refuge constant.
• Prey refuge has no influence on the coexistence of predator and prey species.
• Prey refuge and predator mutual interference could influence population density.

A Lotka–Volterra predator–prey model incorporating a constant number of prey using refuges and mutual interference for predator species is presented. By applying the divergency criterion and theories on exceptional directions and normal sectors, we show that the interior equilibrium is always globally asymptotically stable and two boundary equilibria are both saddle points. Our results indicate that prey refuge has no influence on the coexistence of predator and prey species of the considered model under the effects of mutual interference for predator species, which differently from the conclusion without predator mutual interference, thus improving some known ones. Numerical simulations are performed to illustrate the validity of our results.