In this paper, we study the spreading speed in an integrodifference system which models invasion of predators into the habitat of the prey. Without the requirement of comparison principle, we construct several auxiliary integrodifference equations and use the results of monotone scalar equations to estimate the spreading speed of the invading predators. We also present some numerical simulations to support our theoretical results and demonstrate that the integrodifference predator–prey system exhibits very complex dynamics. Our theory and numerical results imply that the invasion of predators may have a rough constant speed. Moreover, our numerical simulations indicate that the spatial contact of individuals and the overcompensatory phenomenon of the prey may be conducive to the persistence of nonmonotone biological systems and lead to instability of the predator-free state.

中文翻译：

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无比较原理的积分差分捕食者-猎物系统中的传播速度

在本文中，我们研究了一个积分差异系统中的传播速度，该系统模拟了捕食者对猎物栖息地的入侵。在不要求比较原理的情况下，我们构造了几个辅助积分差分方程，并利用单调标量方程的结果来估计入侵掠食者的传播速度。我们还提供了一些数值模拟来支持我们的理论结果，并证明积分差分捕食者 - 猎物系统表现出非常复杂的动力学。我们的理论和数值结果表明捕食者的入侵可能有一个大致恒定的速度。而且，