Mathematics Colloquium

Poster - Mathematics colloquium
Date
to
Location
Teaching and Learning Building, Room 10-4044
Campus
Prince George
This talk explores far-from-equilibrium structures in reaction-diffusion systems, applying asymptotic methods to analyze pattern formation in ecology and biology.  Topics include how patterned vegetation can serve as refuges, preventing extinction under stress in semi-arid regions, and the effects of domain growth on localized pattern generation, a key issue in developmental biology.

Please join us for The Department of Mathematics & Statistics Colloquium

  Chunyi Gai, PhD.

 Department of Mathematics & Statistics

The University of Northern British Columbia

Thursday March20th, 2025

10:30- 11:30 PM

10-4044

Beyond Turing: Far-From-Equilibrium Patterns in Reaction Diffusion Systems
 

Abstract: 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.

Bio:  Dr. Chunyi Gai is an Assistant Professor in the Department of Mathematics and Statistics at UNBC. She joined UNBC in September 2024 after a postdoctoral fellowship at UBC and earning her PhD from Dalhousie University in 2021. Her research focuses on developing new theoretical methods and analyzing real-world problems, including pattern formation in ecology, epidemiology, morphogenesis, and crime. She employs both analytical and numerical techniques to study bifurcations, the stability of localized patterns, and the role of randomness in dynamical systems.

 

 Light refreshments will be served.