Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation
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Título: | Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation |
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Autor/es: | Medjahdi, Ikram | Lachachi, Fatima Zohra | Castro, María Ángeles | Rodríguez, Francisco |
Grupo/s de investigación o GITE: | Modelización de Procesos en Biogeociencias y Ecuaciones Diferenciales con Retardo (MODDE) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemática Aplicada |
Palabras clave: | Vegetation pattern | Stability and bifurcations | Gamma-distributed delay | Turing space |
Fecha de publicación: | 14-may-2024 |
Editor: | MDPI |
Cita bibliográfica: | Symmetry. 2024, 16(5): 609. https://doi.org/10.3390/sym16050609 |
Resumen: | The Klausmeier–Gray–Scott model of vegetation dynamics consists of a system of two partial differential equations relating plant growth and soil water. It is capable of reproducing the characteristic spatial patterns of vegetation found in plant ecosystems under water limitations. Recently, a discrete delay was incorporated into this model to account for the lag between water infiltration into the soil and the following water uptake by plants. In this work, we consider a more ecologically realistic distributed delay to relate plant growth and soil water availability and analyse the effects of different delay types on the dynamics of both mean-field and spatial Klausmeier–Gray–Scott models. We consider distributed delays based on Gamma kernels and use the so-called linear chain trick to analyse the stability of the uniformly vegetated equilibrium. It is shown that the presence of delays can lead to the loss of stability in the constant equilibrium and to a reduction of the parameter region where steady-state vegetation patterns can arise through symmetry-breaking by diffusion-driven instability. However, these effects depend on the type of delay, and they are absent for distributed delays with weak kernels when vegetation mortality is low. |
Patrocinador/es: | This research was funded by “MCIN/AEI/10.13039/501100011033 (Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación) grant number PID2021-125517OB-I00” and “Conselleria de Innovación, Universidades, Ciencia y Sociedad Digital, Generalitat Valenciana grant number CIPROM/2021/001”. I. Medjhadi and F.Z. Lachachi were supported by national grants from the Algerian Ministry of Higher Education and Scientific Research. |
URI: | http://hdl.handle.net/10045/142986 |
ISSN: | 2073-8994 |
DOI: | 10.3390/sym16050609 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.3390/sym16050609 |
Aparece en las colecciones: | INV - MODDE - Artículos de Revistas |
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