This talk consists of introduction to the basic theories on geometric singular perturbation (GSP), and their applications to a generalized Leslie predator-predator model and to an ecological model with diffusion. Adopting different approaches to them, we find several new dynamical phenomena. The study to these models also induces several theoretic problems to be solved in GSP. This talk is based on the joint works with Yixuan Wang in [J Nonlinear Science 2026] and with Qi Qiao and Baodong Zhang in [J London Math Soc 2026].

张祥， 上海交通大学特聘教授、二级教授、 享受国务院特殊津贴专家 、 欧洲科学与艺术院院士。 教育部新世纪优秀人才、 上海市曙光人才计划和浦江人才计划。 主要从事动力系统的定性、 分支和可积理论的研究。主要结果发表在 Adv. Math., American J. Math., Comm. Math. Phys., J. Functional Analysis, J. London. Math. Soc., Trans. Amer. Math. Soc.等国际数学核心期刊上。目前担任动力系统的国际 SCI 杂志 IJBC 和 QTDS 的Associate 编委。