Abstract
This paper deals with the positive solutions of a predator–prey model with additive Allee effect under Neumann boundary conditions. By applying the bifurcation theory, we provide a proof of the existence of local bifurcation solutions and describe the global behavior of these solutions. The result shows that the bifurcation curves can be extended infinitely along [Formula: see text] in the one-dimensional case. Moreover, the limiting behavior of the steady states is clarified using a shadow system approach. It appears that the shadow system exists with a positive solution and it can go into a terminal point when the parameter [Formula: see text] is sufficiently large.
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