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.

本文研究了捕食者-猎物积分差分系统中行波解的最小波速。即使捕食者消失，相应的猎物标量方程也可能是非单调的。在这个耦合系统中没有经典比较原理的假设，我们研究了模拟捕食者入侵猎物栖息地过程的行波解决方案。通过显示非常量行波解的存在和不存在，确定了行波解的最小波速。为了达到这个目的，我们利用构造广义上下解、引入辅助方程和应用标量方程传播理论的方法。