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UBC Theses and Dissertations

The stability of spot patterns for the Brusselator reaction-diffusion system in two space dimensions : periodic and finite domain settings Chang, Yifan


In this thesis, we construct spot equilibrium asymptotic solutions to the Bruusselator model in the semi-strong interaction regime characterized by an asymptotically large diffusivity ratio under two settings: periodic solutions in R² with respect to a Bravais lattice and spot solutions concentrate around some discrete points inside a finite domain. We use matched asymptotic methods, Bloch theory and the study of certain nonlocal eigenvalue problems to do the stability analysis of the linearised system and calculate the two term asymptotic approximation for the stability threshold. In the end we compare the numerical results with the asymptotic approximations, use Ewald’s methods to derive an explicit expression for the regular part of the Bloch Green function to decide the optimal lattice arrangement and do a case study for the N-peak solutions on a ring inside the unite disk.

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