Article
| Title: | Analysis of pattern formation using numerical continuation (English) |
| Author: | Janovský, Vladimír |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 67 |
| Issue: | 6 |
| Year: | 2022 |
| Pages: | 705-726 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | pattern formation |
| Keyword: | reaction-diffusion model |
| Keyword: | Turing instability |
| Keyword: | diffusion-driven instability |
| Keyword: | bifurcation |
| MSC: | 34B24 |
| MSC: | 35B36 |
| MSC: | 35K57 |
| MSC: | 92C15 |
| idZBL: | Zbl 07613020 |
| idMR: | MR4505701 |
| DOI: | 10.21136/AM.2022.0126-21 |
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| Date available: | 2022-10-31T13:25:31Z |
| Last updated: | 2023-11-24 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151053 |
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