Geodesic
Analysis of pattern formation using numerical continuation
Applications of Mathematics, Tome 67 (2022) no. 6, pp. 705-726

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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.
DOI : 10.21136/AM.2022.0126-21
Classification : 34B24, 35B36, 35K57, 92C15
Keywords: pattern formation; reaction-diffusion model; Turing instability; diffusion-driven instability; bifurcation 
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     title = {Analysis of pattern formation using numerical continuation},
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Janovský, Vladimír. Analysis of pattern formation using numerical continuation. Applications of Mathematics, Tome 67 (2022) no. 6, pp. 705-726. doi: 10.21136/AM.2022.0126-21

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