Applications of Mathematics, Vol. 67, No. 6, pp. 705-726, 2022
Analysis of pattern formation using numerical continuation
Vladimír Janovský
Received May 30, 2021. Published online May 2, 2022.
Abstract: The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter $L$, which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries. We define and classify them. Our goal is to calculate a global bifurcation diagram.
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Affiliations: Vladimír Janovský, Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 49/83, 186 75 Praha 8, Czech Republic, e-mail: janovsky@karlin.mff.cuni.cz
