论文标题
共生分支模型：二元性和界面
The symbiotic branching model: duality and interfaces
论文作者
论文摘要
共生分支模型描述了空间两种群体的动力学，其中局部粒子以另一种类型的频率与最接近邻居迁移的频率给出的速率分支。该模型将各种经典模型概括为种群动态，例如垫脚石模型和相互催化的分支模型。我们特别感兴趣地了解共存区域，即两种类型之间的接口。在本章中，我们对我们的结果进行了概述，这些结果描述了这些界面的动力学大规模的动力学。该系统之所以可以解决的原因之一是它表现出丰富的双重性理论。因此，与此同时，我们借此机会在空间人群模型的背景下介绍了二元方法的强度。
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes various classic models in population dynamics, such as the stepping stone model and the mutually catalytic branching model. We are particularly interested in understanding the region of coexistence, i.e. the interface between the two types. In this chapter, we give an overview over our results that describe the dynamics of these interfaces at large scales. One of the reasons that this system is tractable is that it exhibits a rich duality theory. So at the same time, we take the opportunity to provide an introduction to the strength of duality methods in the context of spatial population models.
