Coexistence States in a Prey-Taxis System with a Functional Response Reflecting the Cooperation Effects

This study investigates a prey-taxis system with a functional response reflecting the cooperation effects proposed by [ Cosner et al. , 1999 ]. Under homogeneous Dirichlet boundary conditions, the existence and nonexistence of coexistence states and global bifurcation branches are examined. Our mathematical analysis relies on a priori bounds, principal eigenvalue theory, homogenization technique and global bifurcation method. This leads us to study the coexistence region and compare our results to the prey-taxis system with linear functional response. Our results suggest that the new functional response reduces the likelihood of predator–prey coexistence.