Recent developments on a singular predator-prey model

This work is concerned with the dynamical behaviors of a singular predator-prey model. We first review some well-known results obtained recently. Then we give some new results on the spreading speed of the predator, the existence vs non-existence of traveling waves connecting the predator-free state to the co-existence state, and the existence vs non-existence of spatially periodic traveling waves to this singular predator-prey system.