| 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. |
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