Pattern formation and qualitative analysis for a vegetation-water model with diffusion

In this paper, a diffusive vegetation-water model under Neumann boundary conditions is considered. Firstly, the stability and the diffusion-induced Turing instability are studied. Then, some a priori estimates of positive steady-state solutions are obtained by the maximum principle. Moreover, the bi...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 76; p. 104008
Main Authors Guo, Gaihui, Wang, Jingjing
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2024
Subjects
Double eigenvalue
Steady-state bifurcation
Turing instability
Vegetation pattern
Vegetation-water model
Steady-state bifurcation
Vegetation pattern
Turing instability
Vegetation-water model
Double eigenvalue
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Summary:In this paper, a diffusive vegetation-water model under Neumann boundary conditions is considered. Firstly, the stability and the diffusion-induced Turing instability are studied. Then, some a priori estimates of positive steady-state solutions are obtained by the maximum principle. Moreover, the bifurcations at both simple and double eigenvalues are investigated in detail. Finally, numerical simulations are shown to support and supplement theoretical analysis results. In particular, the evolution processes of vegetation patterns are depicted under different parameters.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2023.104008