The study of spatially explicit integro-difference systems when the local population dynamics are given in terms of discrete-time generations models has gained considerable attention over the past two decades. These nonlinear systems arise naturally in the study of the spatial dispersal of organisms. The brunt of the mathematical research on these systems, particularly, when dealing with cooperative systems, has focused on the study of the existence of traveling wave solutions and the characterization of their spreading speed. Here, we characterize the minimum propagation (spreading) speed, via the convergence of initial data to wave solutions, for a large class of non cooperative nonlinear systems of integro-difference equations. The spreading speed turns out to be the slowest speed from a family of non-constant traveling wave solutions. The applicability of these theoretical results is illustrated through the explicit study of an integro-difference system with local population dynamics governed by Hassell and Comins' non-cooperative competition model (1976). The corresponding integro-difference nonlinear systems that results from the redistribution of individuals via a dispersal kernel is shown to satisfy conditions that guarantee the existence of minimum speeds and traveling waves. This paper is dedicated to Avner Friedman as we celebrate his immense contributions to the fields of partial differential equations, integral equations, mathematical biology, industrial mathematics and applied mathematics in general. His leadership in the mathematical sciences and his mentorship of students and friends over several decades has made a huge difference in the personal and professional lives of many, including both of us.

中文翻译：

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非合作积分差分系统的传播速度和行进波。

在过去的 20 年中，当根据离散时间生成模型给出局部人口动态时，对空间显式积分差分系统的研究引起了相当大的关注。这些非线性系统在研究生物体的空间扩散时自然而然地出现。对这些系统的数学研究首当其冲，尤其是在处理协作系统时，主要集中在研究行波解的存在性及其传播速度的表征上。在这里，我们通过初始数据收敛到波解来表征一大类非合作非线性积分差分方程系统的最小传播（扩展）速度。事实证明，传播速度是非恒定行波解决方案系列中最慢的速度。这些理论结果的适用性通过对具有由 Hassell 和 Comins 的非合作竞争模型（1976）控制的局部人口动态的积分差分系统的明确研究得到说明。相应的积分差分非线性系统是由个体通过分散核重新分布产生的，它满足保证最小速度和行波存在的条件。这篇论文是献给 Avner Friedman 的，因为我们庆祝他在偏微分方程、积分方程、数学生物学、工业数学和一般应用数学领域的巨大贡献。