Global bifurcation of coexistence states for a prey-predator model with prey-taxis/predator-taxis

Abstract This article is concerned with the stationary problem for a prey-predator model prey-taxis/predator-taxis under homogeneous Dirichlet boundary conditions, where interaction governed by Beddington-DeAngelis functional response. We make detailed description of global bifurcation structure coexistence states and find ranges parameters which there exist states. At same time, some sufficient conditions nonexistence are also established. Our method analysis uses idea developed Cintra et al. ( Unilateral class quasilinear elliptic systems applications , J. Differential Equations 267 (2019), 619–657). results indicate that presence makes mathematical more difficult, response leads to different phenomena.