Global Dynamics of Predator–Prey Systems With Antipredation Strategy in Open Advective Environments

We analyze reaction–diffusion–advection systems with Danckwerts boundary conditions describing the interactions of prey and specialist/generalist predators in open advective environments, in which the cost and benefit of antipredation responses are considered. The existence and stability of semitrivial steady states and positive ones are established via the monotonicity of principal eigenvalues with respect to parameters, priori estimates, and other techniques. Specially, for the specialist predator–prey system, the stability of positive steady states near the semitrivial steady state is proved by the bifurcation and spectral analysis, and we apply the global bifurcation theory to obtain a global bifurcation branch which connects to the positive steady state without fear effect. For the generalist predator–prey system, we establish the global stability of a unique positive steady state by constructing a spatial Lyapunov function. Compared with the case of no fear effect, the results show that antipredation strategy mainly influences the coexistence of both species, and the outcomes for specialist and generalist predators are significantly different. Under small advection rates, high antipredation level can prevent the invasion of specialist predators, while lead to the persistence of generalist predators alone.