Persistence and Pattern Formation in Biological Systems

史研究员发展和研究了种群生态学和生化系统模式形成的一些反应-扩散模型。在低密度下，种群的空间分布会受到增长率下降的影响，这被称为Allee效应。例如，它可能是由于交配不足、缺乏有效的授粉或收获造成的。主要目标是深入了解Allee和收获效应以及扩散行为如何影响物种的持续和灭绝以及生物入侵的成功或失败。发展了非线性椭圆和抛物型偏微分方程组和非线性泛函分析的新的数学工具来研究复杂的动力学。重点讨论了在简化的一维问题中不能通过线性化获得的非线性现象，以及在更高的空间域中不能观察到的模式。该项目以一系列实际问题为指导，包括渔业管理、动物聚集和自催化反应。该项目的第二行集中在模式形成机制上，概括了艾伦·图灵的开创性工作。建立了一种非线性的高维机制来完善图灵模式理论，该机制已成功地应用于唯象模型、经验底物-抑制体系和自催化反应。该项目的一部分研究了人类干扰对海洋物种自然进化的影响。在项目的第二部分，研究人员考虑了在大自然中随处可见的复杂图案的产生，比如贝壳和斑马或豹上的斑点图案。这些研究旨在了解和控制许多重要的自然现象，如商业海洋物种的持续和灭绝，以及生化过程中复杂的模式形成。该项目的成果有助于制定管理商业性渔业和森林的政策，并有助于开发新的生物技术--模拟自然生命形式。

Shi The investigator develops and studies somereaction-diffusion models of population ecology and of patternformations of biochemical systems. The spatial distribution ofpopulations can be affected by depressed growth rate at lowerdensity, which is called the Allee effect. For instance, it canbe caused by shortage of mates, lack of effective pollination,or harvesting. The main goal is to gain insight into the waysthat Allee and harvesting effects and dispersal behaviorinfluence the persistence and extinction of species and thesuccess or failure of biological invasions. New mathematicaltools in nonlinear elliptic and parabolic partial differentialequations and nonlinear functional analysis are developed tostudy the complicated dynamics. Emphasis is on the nonlinearphenomena that can not be obtained through linearization and onpatterns in higher spatial domains that can not be observed insimplified one-dimensional problems. The project is guided by aseries of practical problems, from fishery management, animalaggregation, and autocatalytic reactions. A second line of theproject is focused on a pattern formation mechanism, generalizingthe pioneer work of Alan Turing. A nonlinear and higher spatialdimensional mechanism is established to refine Turing patterntheory, which has been successfully applied to phenomenologicalmodels, empirical substrate-inhibition systems, and autocatalyticreactions. One part of the project studies the impact of humaninterference on the natural evolution of marine species. In thesecond part of the project, the investigator considers the originof the generation of complex patterns found everywhere in thenature, like seashells and spotty patterns on a zebra or aleopard. These studies aim to understand and control manyimportant natural phenomena, such as the persistence andextinction of commercial marine species, and complex patternformations in biochemical processes. Results of the project canbe helpful for formulating policy on managing commercialfisheries and forests, and for developing new biotechnologysimulations of natural life forms.