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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| Published in | Nonlinear analysis: real world applications Vol. 76; p. 104008 |
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| Format | Journal Article |
| Language | English |
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01.04.2024
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 104008 |
| Author | Wang, Jingjing Guo, Gaihui |
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| Cites_doi | 10.1016/0022-1236(71)90030-9 10.1142/S0218127421500383 10.1006/jdeq.1996.0157 10.1007/s11071-020-05486-w 10.1007/s00285-005-0319-5 10.1002/mma.6518 10.1007/s11538-011-9688-7 10.1016/j.cnsns.2016.06.008 10.1016/j.jtbi.2021.110997 10.1006/jfan.1999.3483 10.3934/dcds.2017206 10.1016/j.aml.2019.03.027 10.1016/j.nonrwa.2021.103443 10.1016/j.cnsns.2021.105807 10.1111/sapm.12444 10.1016/j.ecocom.2017.02.005 10.1016/j.jmaa.2020.124860 10.1016/j.cnsns.2022.106644 10.1007/s10884-004-2782-x 10.1126/science.284.5421.1826 10.1007/s11071-013-0935-3 10.1016/j.apm.2018.04.010 10.1016/S0960-0779(03)00049-3 10.1016/0022-1236(71)90015-2 10.1016/j.jfranklin.2018.07.014 10.1142/S0218127422500699 10.1142/S0218127418501407 10.1016/j.physd.2020.132396 10.1137/0513037 10.1016/0022-0396(86)90119-1 |
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| Keywords | Steady-state bifurcation Vegetation pattern Turing instability Vegetation-water model Double eigenvalue |
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| Snippet | In this paper, a diffusive vegetation-water model under Neumann boundary conditions is considered. Firstly, the stability and the diffusion-induced Turing... |
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| SubjectTerms | Double eigenvalue Steady-state bifurcation Turing instability Vegetation pattern Vegetation-water model |
| Title | Pattern formation and qualitative analysis for a vegetation-water model with diffusion |
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