Abstract
This paper studies the minimal wave speed of travelling wave solutions in a predator–prey integrodifference system. Even if the predator vanishes, the corresponding scalar equation of prey may be nonmonotonic. Without the assumption of classical comparison principle in this coupled system, we investigate travelling wave solutions modelling the process that the predator invades the habitat of the prey. By showing the existence and nonexistence of nonconstant travelling wave solutions, the minimal wave speed of travelling wave solutions is confirmed. To achieve the purpose, we utilize recipes of constructing generalized upper and lower solutions, introducing auxiliary equations and applying the propagation theory of scalar equations.
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