Patterns of interacting populations in heterogeneous environments

我的研究计划的目标是机械地了解时间和空间变化对相互作用的种群动态的影响，并研究这种相互作用产生的模式。方法是推导出各种数学模型，并使用分析和数值方法研究它们的行为。这些模型是动力系统，由常微分方程式或偏微分方程式、差分方程式或积分差分方程式或它们的某种组合所给出。这些技术包括线性和非线性分析、齐次化、稳定性理论、行波和数值分析。该计划由几个相互关联的战略和战术研究方向组成，这些方向相互通报并从中受益。

The goal of my research program is to mechanistically understand the effects of temporal and spatial variation on the dynamics of interacting populations and to study the patterns emerging from this interplay. The approach is to derive a variety of mathematical models and to study their behavior using analytical and numerical methods. The models are dynamical systems, given by ordinary or partial differential equations, difference or integrodifference equations, or some combination thereof. The techniques include linear and non-linear analysis, homogenization, stability theory, traveling waves, and numerical analysis. The program consists of several interconnected research directions, strategic and tactical, that inform and benefit from one another.