Existence of localized radial patterns in a model for dryland vegetation

DOI10.1093/IMAMAT/HXAC007zbMATH Open1497.35476arXiv2107.12678OpenAlexW4225695748MaRDI QIDQ5104013

Dan J. Hill

Publication date: 9 September 2022

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Abstract: Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for dryland vegetation on flat terrain. By considering certain prototypical pattern-forming systems, we prove the existence of three classes of localised radial patterns bifurcating from a Turing instability. We also present evidence for the existence of localised gap solutions close to a homogeneous instability. Additionally, we numerically solve the vegetation model and use continuation methods to study the bifurcation structure and radial stability of localised radial spots and gaps. We conclude by investigating the effect of varying certain parameter values on the existence and stability of these localised radial patterns.

Full work available at URL: https://arxiv.org/abs/2107.12678

zbMATH Keywords

bifurcationlocalized patternsradial patternssemi-arid ecosystem

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Developmental biology, pattern formation (92C15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Bifurcations in context of PDEs (35B32) Computational methods for problems pertaining to biology (92-08) Plant biology (92C80)

Related Items (7)

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