Consumer-resource spatiotemporal dynamics with Ivlev-type functional response in open advective environments

This paper investigates a two-species predator–prey model in open advective environments with an Ivlev-type functional response, under Danckwerts boundary conditions. We first analyze the continuity and monotonicity of the principal eigenvalue with respect to parameters, and establish the global stability of trivial and semi-trivial steady states. Next, we provide a complete classification of the long-term behavior of solutions in terms of the advection rate [Formula: see text] and saturation constant [Formula: see text], and prove the existence of the positive steady state when the Ivlev parameter [Formula: see text] is larger.