In this paper,we study a class of predator-prey models with Beddington-De Angelis functional response.And the predator equation has singularity in zero prey population,where a smoothing auxiliary function is introduced to overcome it.Our aim is to see if the predator and prey can eventually survive when an alien predator enters the habitat of an existing prey by employing traveling wave solutions,based on the upper and lower solutions and Schauder’s fixed point theorem.In addition,the non-existence of traveling wave solutions is discussed by the comparison principle.At the same time,some simulations are carried out to further verify the results.
