复杂趋化模型研究初探

A probe into research of complex chemotaxis models

本文试图提供复杂趋化模型的一个研究概览.首先回顾两个著名的信号产出和营养消耗的Keller-Segel模型,然后介绍双退化营养趋向性模型并刻画觅食者和乞讨者两类人口群之间相互作用的趋向性串联模型以及完全交叉扩散的捕食追逃模型的生物背景及其数学研究进展.接下来阐述了完全交叉扩散系统的4阶薄膜型方程逼近的主要思想和关键步骤.最后简要提及其他一些复杂趋化模型.

In this paper,we attempt to provide an overview of the study of complex chemotaxis models.Beginning with recalling the well-known Keller-Segel model with signal-production or with nutrient-consumption,we introduce some biological backgrounds and mathematical research progress of doubly degenerate nutrienttaxis models,taxis-cascaded models describing the interaction between two population groups of foragers and scroungers,and fully cross-diffusive predator-prey pursuit-evasion models.We then present the main ideas and crucial steps in the approximation of fourth-order thin-film-type equations to a fully cross-diffusive system.Finally,we also briefly mention some other complex chemotaxis models.