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In this paper, a diffusive predator–prey model with Holling type II (Michaelis–Menten) functional response and a protection zone for prey is investigated. Dynamics and steady state solutions of the system are analyzed. We give the a priori estimates and obtain the nonexistence of nonconstant positive solution as the diffusion coefficients are large enough. Moreover, we demonstrate the existence and stability of nonconstant steady state solutions branching from constant semi-trivial solution by using bifurcation theory.

Dynamics of Holling-type II prey–predator system with a protection zone for prey