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arXiv · 2405.16927

The role of spatial dimension in the emergence of localised radial patterns from a Turing instability

Dan J. Hill
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Abstract

The emergence of localised 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 localised $(n+1)$-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 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 localised radial patterns in different spatial dimensions.

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Dan J. Hill. 2024-05-27. The role of spatial dimension in the emergence of localised radial patterns from a Turing instability. https://arxiv.org/abs/2405.16927

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