非合作积分差分系统的传播速度和行波
Spreading speeds and traveling waves for non-cooperative integro-difference systems
摘要：
发展宏观描述的联合动力学和行为的大型异质性合奏受生态力，如扩散仍然是一个中心的挑战，数学家和生物科学家一样。在过去的一个世纪里，人们特别关注扩散在形成植物群落方面所起的作用，或海洋开阔洋和潮间带系统的动态，或生物入侵，或疾病的传播，仅举几例。数学家和理论家，开始与努力的研究人员，包括阿伦森，费舍尔，哥洛夫，莱文，大久保，科斯特拉姆，Slobodkin，温伯格和许多其他人，奠定了基础的一个肥沃的研究领域的界面生态学，数学，人口生物学和进化生物学。积分差分系统，本手稿的主题，自然出现在研究的空间扩散的生物体的地方种群动态规定的离散世代的模型。数学研究的重点集中在研究行波解的存在性和传播速度的特征，特别是在合作系统的背景下。在本文中，我们的一大类非合作系统，所有制定的积分差分方程，初始数据的收敛波解的传播速度的特点。在这种情况下，传播速度的特点是一个家庭的非恒定行波解的最慢速度。我们的结果被应用到一个特定的非合作竞争系统的细节。
英文摘要：
The development of macroscopic descriptions for the joint dynamics and behavior of large heterogeneous ensembles subject to ecological forces like dispersal remains a central challenge for mathematicians and biological scientists alike. Over the past century, specific attention has been directed to the role played by dispersal in shaping plant communities, or on the dynamics of marine open-ocean and intertidal systems, or on biological invasions, or on the spread of disease, to name a few. Mathematicians and theoreticians, starting with the efforts of researchers that include Aronson, Fisher, Kolmogorov, Levin, Okubo, Skellam, Slobodkin, Weinberger and many others, set the foundation of a fertile area of research at the interface of ecology, mathematics, population biology and evolutionary biology. Integrodifference systems, the subject of this manuscript, arise naturally in the study of the spatial dispersal of organisms whose local population dynamics are prescribed by models with discrete generations. The brunt of the mathematical research has focused on the the study of existence traveling wave solutions and characterizations of the spreading speed particularly, in the context of cooperative systems. In this paper, we characterize the spreading speed for a large class of non cooperative systems, all formulated in terms of integrodifference equations, by the convergence of initial data to wave solutions. In this setting, the spreading speed is characterized as the slowest speed of a family of non-constant traveling wave solutions. Our results are applied to a specific non-cooperative competition system in detail.
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