Journal article
The role of spatial dimension in the emergence of localized radial patterns from a Turing instability
- Abstract:
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The emergence of localized radial patterns from a Turing instability has been well studied in two- and three-dimensional settings and predicted for higher spatial dimensions. We prove the existence of localized (𝑛+1)-dimensional radial patterns in general two-component reaction–diffusion systems near a Turing instability, where 𝑛>0 is taken to be a continuous parameter. We determine the explicit dependence of each pattern’s radial profile on the dimension 𝑛 through the introduction of (𝑛+1)-dimensional Bessel functions, revealing a deep connection between the formation of localized radial patterns in different spatial dimensions.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
-
-
(Preview, Accepted manuscript, pdf, 2.9MB, Terms of use)
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- Publisher copy:
- 10.1098/rspa.2024.0400
Authors
- Publisher:
- Royal Society
- Journal:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences More from this journal
- Volume:
- 480
- Issue:
- 2304
- Article number:
- 20240400
- Publication date:
- 2024-12-11
- Acceptance date:
- 2024-10-10
- DOI:
- EISSN:
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1471-2946
- ISSN:
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1364-5021
- Language:
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English
- Pubs id:
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2286804
- Local pid:
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pubs:2286804
- Deposit date:
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2025-09-08
Terms of use
- Copyright holder:
- Dan J Hill
- Copyright date:
- 2024
- Rights statement:
- © 2024 The Author(s). Published by the Royal Society. All rights reserved.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Royal Society at https://dx.doi.org/10.1098/rspa.2024.0400
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