Propagation Dynamics in a Predator-Prey Model with Harvesting and Hyperbolic Mortality

In this study, we consider a diffusive predator-prey system with hyperbolic mortality for predators and nonlinear harvesting for prey. First, the existence of traveling wave solutions is established by applying the method of upper and lower solutions together with the squeeze technique, which connects the predator-free constant steady state and the coexistence steady state. Second, using Hopf bifurcation theorem, we also prove the existence of small amplitude periodic traveling wave trains. The obtained traveling wave solution suggests that the predator invasion results in periodic oscillations in the population coexistence domain.