题目：My journey to Mathematical Ecology
报告人： 许世壁教授 台湾清华大学
摘要：In this talk I shall share with the audience my personal research experience in Mathematical Ecology in the past forty years. One of the central questions in Mathematical Ecology is to understand biodiversity and coexistence of the species. Various temporal and spatial mathematical models are constructed to explain the phenomena of coexistence of species observed in nature. These models also brought new facinating research topics in differential equations and dynamical systems.
First I shall introduce the mathematical models in chemostat. The k resources-n consumers interactions are used to describe the mechanisms of competition among the species. The resources will include nutrients and light and the consumers will be phytoplankton species. These models are formulated in ODE. However in nature, we shall consider the PDE models in a water column.
The second part is to consider the models in general ecology. We shall discuss the mathematical models of predator-prey systems , food chain systems and n species competition systems. In addition to regular dynamics, we may have chaotic dynamics.
Mathematical challenges in these topics are to prove the global dynamics for example the global stability of equilibrium, uniqueness of limit cycles, existence of periodic solutions and uniform persistence. Various applications of monotone dynamical systems will be discussed, especially the general frame of two species competition in ordered Banach spaces.