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

2024/05/27 by Dan J. Hill, Hill, Dan J. · 1 citation
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.2405.16927

openalex publication_date 2024/05/27 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

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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• Global bifurcation of localised 2D patterns emerging from spatial heterogeneity

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