主讲人：盖春奕

主讲人简介：盖春奕，加拿大北英属哥伦比亚大学（UNBC）助理教授，2021年获达尔豪斯大学数学博士学位。2021年至2024年期间担任英属哥伦比亚大学（UBC）的博士后研究员。目前的研究领域为动力系统理论及应用分析，特别关注利用渐近分析和奇异摄动技术研究反应扩散系统中的斑图形成、分支分析和局部斑图的稳定性分析，注重理解随机性的作用及其对动力系统的影响。主要研究成果先后发表在SIAM Journal on Applied Dynamical Systems, SIAM Journal on Applied Mathematics, Proceedings of the Royal Society A, Discrete and Continuous Dynamical Systems等杂志。

报告内容概要：Natural patterns are ubiquitous, yet understanding their formation remains a puzzle. In this talk, I explore the dynamics and stability of localized patterns within various reaction-diffusion systems. Since these patterns are "far-from-equilibrium" structures, the classical Turing-type stability analysis is not applicable. Instead, I apply the method of matched asymptotic expansions and nonlocal eigenvalue problems to analyze these singularly perturbed PDEs. I will demonstrate two applications arising from mathematical ecology and biology. The first example describes how patterned states can provide a refuge and prevent extinction under stressed conditions. It also illustrates the importance of not only the absolute level of climate change, but also the speed with which it occurs. The second application focuses on the influence of domain growth on pattern formation, a key issue in developmental biology. In particular, the analysis reveals two primary mechanisms-spike self-replication and spike nucleation, and is confirmed by numerical simulation and continuation.