Dpto. de Matematicas, Universidad de Oviedo, c/ Calvo Sotelo, 33007-Oviedo, Spain.
Math Biosci Eng. 2013 Jun;10(3):637-47. doi: 10.3934/mbe.2013.10.637.
In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. Apart from competitive Lotka-Volterra (reaction) and population pressure (cross-diffusion) terms, a convective term modeling the populations attraction to more favorable environmental regions was included. In this article, we study numerically a modification of their convective term to take account for the notion of spatial adaptation of populations. After describing the model, in which a time non-local drift term is considered, we propose a numerical discretization in terms of a mass-preserving time semi-implicit finite element method. Finally, we provied the results of some biologically inspired numerical experiments showing qualitative differences between the original model of [18] and the model proposed in this article.
在[18]中，Sighesada、川崎和寺本提出了一个用于模拟相互作用物种空间隔离的偏微分方程组系统。除了竞争的Lotka-Volterra（反应）和种群压力（交叉扩散）项外，还包括一个对流项，用于模拟种群对更有利环境区域的吸引力。在本文中，我们对他们的对流项进行了数值研究，以考虑种群的空间适应性概念。在描述了模型之后，其中考虑了一个非局部的时变漂移项，我们提出了一个基于质量守恒的时间半隐式有限元方法的数值离散化方法。最后，我们提供了一些具有生物学启发的数值实验的结果，这些结果表明了[18]中的原始模型和本文中提出的模型之间的定性差异。
