Special Session 84: Mathematical modeling and analysis in spatial ecology and epidemiology

Equivariant Turing-Turing Bifurcations and Pattern Formation on a Square Domain
Hongbin Wang
School of Mathematics, Harbin Institute of Technology
Peoples Rep of China
Co-Author(s):    Chen Chen
Abstract:
In this talk, I would like to report one of our recent works on equivariant Turing-Turing bifurcations and pattern formation in square spatial domains. For a relatively general reaction-diffusion systems with self-diffusion and cross-diffusion terms, we derive the local center manifolds near equivariant Turing-Turing singularities. We give approximate expressions for superposition-type steady states and their stability conditions. As an application, we analyze a plant-water interaction model to explore the formation of self-organized vegetation patterns in semi-arid regions.