Coexistence states for a class of prey–predator models with population flux by attractive transition

This paper concerns a class of prey–predator models with population flux by attractive transition under homogeneous Dirichlet boundary conditions, which is a modification of the model proposed by Kuto and Odea (Kuto and Oeda, 2022; Oeda and Kuto, 2018). We give the necessary and sufficient conditions for the existence of coexistence states. The mathematical analysis relies on an a priori estimate result and a global bifurcation method. Compared with the previous works (Kuto and Oeda, 2022; Oeda and Kuto, 2018), there are essential differences in establishing an a priori estimate result.