Persistence and Pattern Formation in Biological Systems

石 研究者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生长速率降低的影响，这就是所谓的Allee效应。 例如，它可能是由于缺少配偶，缺乏有效的授粉，或收获。 主要目标是深入了解Allee和收获效应以及扩散行为影响物种持续存在和灭绝以及生物入侵成功或失败的方式。 在非线性椭圆和抛物型偏微分方程和非线性泛函分析中发展了新的分析工具来研究复杂的动力学。 重点是不能通过线性化获得的非线性现象和在更高空间域中不能在简化的一维问题中观察到的模式。 该项目由一系列实际问题指导，从渔业管理，动物聚集和自催化反应。 该项目的第二条线集中在模式形成机制上，概括了艾伦·图灵的先驱工作。 建立了一个非线性和更高空间维的机制来完善图灵模式理论，该理论已成功地应用于唯象模型、经验底物抑制系统和自催化反应。 该项目的一部分研究人类干扰对海洋物种自然进化的影响。 在项目的第二部分，研究人员考虑了自然界中随处可见的复杂图案的起源，比如贝壳和斑马或蝴蝶身上的斑点图案。 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久性和灭绝，以及生物化学过程中的复杂模式形成。 该项目的结果有助于制定管理商业渔业和森林的政策，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.