Pattern dynamics of a vegetation-water model with saturated effect and diffusion feedback

Desertification represents one of the most pressing ecological challenges globally, where vegetation patterns serve as critical indicators of ecosystem resilience and early-warning signatures of ecological degradation. Soil water diffusive feedbacks and saturation water uptake by vegetation are impo...

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Veröffentlicht in:Physica A Jg. 673; S. 130676
Hauptverfasser: Bai, Huimin, Fan, Yu-Xuan, Li, Li
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.09.2025
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Abstract Desertification represents one of the most pressing ecological challenges globally, where vegetation patterns serve as critical indicators of ecosystem resilience and early-warning signatures of ecological degradation. Soil water diffusive feedbacks and saturation water uptake by vegetation are important mechanisms for vegetation-water interactions in arid and semi-arid environments. In this paper, a Klausmeier-type vegetation-water model is investigated to study the mechanism of vegetation pattern formation by incorporating a saturated water absorption term and soil water diffusion feedback. We derive amplitude equations near the Turing bifurcation point, revealing selection criteria and stability conditions for vegetation patterns. Our findings reveal that the saturated water absorption effect induces pattern phase transitions, the feedback mechanism of soil water diffusion accelerates desertification, and precipitation gradients induce the emergence of a bistable coexistence phenomenon. These results provide theoretical insights into the dynamics of vegetation patterns and offer guidance for ecosystem management and desertification control.
AbstractList Desertification represents one of the most pressing ecological challenges globally, where vegetation patterns serve as critical indicators of ecosystem resilience and early-warning signatures of ecological degradation. Soil water diffusive feedbacks and saturation water uptake by vegetation are important mechanisms for vegetation-water interactions in arid and semi-arid environments. In this paper, a Klausmeier-type vegetation-water model is investigated to study the mechanism of vegetation pattern formation by incorporating a saturated water absorption term and soil water diffusion feedback. We derive amplitude equations near the Turing bifurcation point, revealing selection criteria and stability conditions for vegetation patterns. Our findings reveal that the saturated water absorption effect induces pattern phase transitions, the feedback mechanism of soil water diffusion accelerates desertification, and precipitation gradients induce the emergence of a bistable coexistence phenomenon. These results provide theoretical insights into the dynamics of vegetation patterns and offer guidance for ecosystem management and desertification control.
ArticleNumber 130676
Author Bai, Huimin
Li, Li
Fan, Yu-Xuan
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  organization: Department of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
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  givenname: Yu-Xuan
  surname: Fan
  fullname: Fan, Yu-Xuan
  organization: Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, China
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  givenname: Li
  surname: Li
  fullname: Li, Li
  email: lili831113@sxu.edu.cn
  organization: School of Computer and Information Technology, Shanxi University, Taiyuan 030006, Shanxi, China
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Cites_doi 10.1007/s00285-022-01825-0
10.1051/mmnp/20116109
10.1016/j.tpb.2008.09.004
10.1126/science.1082750
10.1126/science.284.5421.1826
10.1016/j.jtbi.2006.08.006
10.1016/j.jtbi.2008.05.017
10.1088/0951-7715/23/10/016
10.1002/qua.10878
10.1007/s11538-011-9688-7
10.1137/120862648
10.1098/rspa.2011.0194
10.1007/BF02462004
10.1073/pnas.2305153121
10.1038/nclimate3275
10.1007/s11071-024-09500-3
10.1890/0012-9658(2001)082[0050:VPFISA]2.0.CO;2
10.1002/mma.10480
10.1126/science.abj0359
10.1063/PT.3.4340
10.1016/j.physd.2012.08.014
10.1007/s11071-016-2671-y
10.1073/pnas.1522130113
10.1016/j.ecolind.2018.03.083
10.3390/rs14061307
10.1007/s00332-012-9139-0
10.1038/nclimate2837
10.1038/s41598-017-02619-x
10.1016/j.plrev.2022.09.005
10.1111/sapm.12482
10.1016/j.cnsns.2023.107802
10.1098/rsta.2012.0358
10.1016/j.catena.2019.104095
10.1103/PhysRevE.85.021924
10.1073/pnas.2306514120
10.1029/2007RG000256
10.1007/BF00289234
10.1103/PhysRevLett.87.198101
10.1137/120899510
10.1016/j.chaos.2024.114622
10.1016/j.agrformet.2017.11.013
10.3389/fphy.2021.721115
10.1016/j.apm.2018.04.010
10.1371/journal.pone.0092097
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Keywords Soil water diffusion feedback
Multi-scale analysis
Bifurcation phenomena
Vegetation patterns
Saturation water absorption effect
Language English
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References Meron (b17) 2019; 72
Gierer, Meinhardt (b23) 1972; 12
Liu, Jin, Li (b34) 2008; 254
Huang, Yu, Dai, Wei, Kang (b2) 2017; 7
Meron (b16) 2015; vol. 10
Gilad, von Hardenberg, Provenzale, Shachak, Meron (b10) 2007; 244
Klausmeier (b7) 1999; 284
Guo, You, Ahmed Abbakar (b19) 2025; 48
Liang, Sun (b21) 2024; 14
Getzin, Yizhaq, Bell, Erickson, Postle, Katra, Tzuk, Zelnik, Wiegand, Wiegand, Meron (b36) 2016; 113
Lefever, Lejeune (b22) 1997; 59
Liang, Li, Cui (b40) 2021; 38
Guo, Qin, Pang, Su (b42) 2024; 131
Sun, Li, Li, Liu, Wu, Gao, Wang, Feng (b8) 2022; 43
Sun (b47) 2016; 85
Zhang, Sun, Jin (b46) 2012; 85
Nemani, Keeling, Hashimoto, Jolly, Piper, Tucker, Myneni, Running (b12) 2003; 300
Zhao, Dai, Dong (b13) 2018; 249
van der Stelt, Doelman, Hek, Rademacher (b29) 2013; 23
Guo, Qin, Cao, Jia, Pang (b43) 2024; 181
Huang, Yu, Guan, Wang, Guo (b1) 2016; 6
Kealy, Wollkind (b20) 2012; 74
Liang, Sun (b31) 2024; 112
HilleRisLambers, Rietkerk, van den Bosch, Prins, de Kroon (b9) 2001; 82
Sherratt (b27) 2013; 73
Chen, Hu, Nie, Wang (b39) 2017; 7
Ge (b5) 2023; 120
Sherratt (b26) 2013; 242
Sun, Wang, Chang, Wu, Li, Jin (b35) 2018; 61
Sherratt (b24) 2010; 23
Sherratt (b25) 2011; 467
Chang, Li, Li, Xiao, Zhao, Su, Feng (b38) 2019; 181
Kefi, Rietkerk, Katul (b30) 2008; 74
Li, Cao, Bao (b41) 2021; 9
Kéfi, Guttal, Brock, Carpenter, Ellison, Livina, Seekell, Scheffer, Van Nes, Dakos (b3) 2014; 9
Bai, Gong, Sun, Li (b14) 2022; 14
Rietkerk, Bastiaansen, Banerjee, van de Koppel, Baudena, Doelman (b4) 2021; 374
Kéfi, Génin, Garcia-Mayor, Guirado, Cabral, Berdugo, Guerber, Solé, Maestre (b6) 2024; 121
Liu, Yu, Jia (b37) 2018; 91
Li, Sun, Guo (b32) 2022; 148
von Hardenberg, Meron, Shachak, Zarmi (b18) 2001; 87
Sherratt (b28) 2013; 73
Sun, Hou, Li, Jin, Wang (b44) 2022; 85
Lejeune, Tlidi, Lefever (b45) 2004; 98
Zelnik, Kinast, Yizhaq, Bel, Meron (b33) 2013; 371
Borgogno, D’odorico, Laio, Ridolfi (b11) 2009; 47
Meron (b15) 2011; 6
Huang (10.1016/j.physa.2025.130676_b1) 2016; 6
Gilad (10.1016/j.physa.2025.130676_b10) 2007; 244
van der Stelt (10.1016/j.physa.2025.130676_b29) 2013; 23
Sun (10.1016/j.physa.2025.130676_b35) 2018; 61
Sun (10.1016/j.physa.2025.130676_b47) 2016; 85
Zelnik (10.1016/j.physa.2025.130676_b33) 2013; 371
Sherratt (10.1016/j.physa.2025.130676_b24) 2010; 23
Lejeune (10.1016/j.physa.2025.130676_b45) 2004; 98
Sun (10.1016/j.physa.2025.130676_b8) 2022; 43
Borgogno (10.1016/j.physa.2025.130676_b11) 2009; 47
Gierer (10.1016/j.physa.2025.130676_b23) 1972; 12
Li (10.1016/j.physa.2025.130676_b32) 2022; 148
Guo (10.1016/j.physa.2025.130676_b43) 2024; 181
Sherratt (10.1016/j.physa.2025.130676_b27) 2013; 73
HilleRisLambers (10.1016/j.physa.2025.130676_b9) 2001; 82
Liang (10.1016/j.physa.2025.130676_b31) 2024; 112
Meron (10.1016/j.physa.2025.130676_b17) 2019; 72
Guo (10.1016/j.physa.2025.130676_b19) 2025; 48
Sun (10.1016/j.physa.2025.130676_b44) 2022; 85
Rietkerk (10.1016/j.physa.2025.130676_b4) 2021; 374
Huang (10.1016/j.physa.2025.130676_b2) 2017; 7
Liu (10.1016/j.physa.2025.130676_b34) 2008; 254
Chang (10.1016/j.physa.2025.130676_b38) 2019; 181
Guo (10.1016/j.physa.2025.130676_b42) 2024; 131
Kéfi (10.1016/j.physa.2025.130676_b6) 2024; 121
Sherratt (10.1016/j.physa.2025.130676_b28) 2013; 73
Nemani (10.1016/j.physa.2025.130676_b12) 2003; 300
Liu (10.1016/j.physa.2025.130676_b37) 2018; 91
Lefever (10.1016/j.physa.2025.130676_b22) 1997; 59
Kéfi (10.1016/j.physa.2025.130676_b3) 2014; 9
Getzin (10.1016/j.physa.2025.130676_b36) 2016; 113
Meron (10.1016/j.physa.2025.130676_b15) 2011; 6
Kealy (10.1016/j.physa.2025.130676_b20) 2012; 74
Sherratt (10.1016/j.physa.2025.130676_b26) 2013; 242
Liang (10.1016/j.physa.2025.130676_b40) 2021; 38
Chen (10.1016/j.physa.2025.130676_b39) 2017; 7
Ge (10.1016/j.physa.2025.130676_b5) 2023; 120
Klausmeier (10.1016/j.physa.2025.130676_b7) 1999; 284
Zhao (10.1016/j.physa.2025.130676_b13) 2018; 249
Kefi (10.1016/j.physa.2025.130676_b30) 2008; 74
Zhang (10.1016/j.physa.2025.130676_b46) 2012; 85
Liang (10.1016/j.physa.2025.130676_b21) 2024; 14
Bai (10.1016/j.physa.2025.130676_b14) 2022; 14
Meron (10.1016/j.physa.2025.130676_b16) 2015; vol. 10
Sherratt (10.1016/j.physa.2025.130676_b25) 2011; 467
Li (10.1016/j.physa.2025.130676_b41) 2021; 9
von Hardenberg (10.1016/j.physa.2025.130676_b18) 2001; 87
References_xml – volume: 72
  start-page: 30
  year: 2019
  end-page: 36
  ident: b17
  article-title: Vegetation pattern formation: The mechanisms behind the forms
  publication-title: Phys. Today
– volume: 73
  start-page: 330
  year: 2013
  end-page: 350
  ident: b27
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments IV: slowly moving patterns and their stability
  publication-title: SIAM J. Appl. Math.
– volume: 244
  start-page: 680
  year: 2007
  end-page: 691
  ident: b10
  article-title: A mathematical model of plants as ecosystem engineers
  publication-title: J. Theoret. Biol.
– volume: 374
  start-page: eabj0359
  year: 2021
  ident: b4
  article-title: Evasion of tipping in complex systems through spatial pattern formation
  publication-title: Science
– volume: 14
  start-page: 473
  year: 2024
  end-page: 505
  ident: b21
  article-title: Effect of nonlocal delay with strong kernel on vegetation pattern
  publication-title: J. Appl. Anal. Comput.
– volume: 48
  start-page: 3190
  year: 2025
  end-page: 3213
  ident: b19
  article-title: Pattern dynamics in a water–vegetation model with cross-diffusion and nonlocal delay
  publication-title: Math. Methods Appl. Sci.
– volume: 23
  start-page: 39
  year: 2013
  end-page: 95
  ident: b29
  article-title: Rise and fall of periodic patterns for a generalized Klausmeier–Gray–Scott model
  publication-title: J. Nonlinear Sci.
– volume: 249
  start-page: 198
  year: 2018
  end-page: 209
  ident: b13
  article-title: Changes in global vegetation activity and its driving factors during 1982–2013
  publication-title: Agricult. Forest. Meterol.
– volume: 59
  start-page: 263
  year: 1997
  end-page: 294
  ident: b22
  article-title: On the origin of tiger bush
  publication-title: Bull. Math. Biol.
– volume: 91
  start-page: 249
  year: 2018
  end-page: 258
  ident: b37
  article-title: Water utilization characteristics of typical vegetation in the rocky mountain area of Beijing, China
  publication-title: Ecol. Indic.
– volume: 12
  start-page: 30
  year: 1972
  end-page: 39
  ident: b23
  article-title: A theory of biological pattern formation
  publication-title: Kybernetik
– volume: 23
  start-page: 2657
  year: 2010
  ident: b24
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments I
  publication-title: Nonlinearity
– volume: 43
  start-page: 239
  year: 2022
  end-page: 270
  ident: b8
  article-title: Impacts of climate change on vegetation pattern: Mathematical modeling and data analysis
  publication-title: Phys. Life Rev.
– volume: 112
  start-page: 8675
  year: 2024
  end-page: 8693
  ident: b31
  article-title: Effects of climate change on vegetation pattern in Baotou, China
  publication-title: Nonlinear Dynam.
– volume: 9
  year: 2021
  ident: b41
  article-title: Pattern dynamics of vegetation growth with saturated water absorption
  publication-title: Front. Phys.
– volume: 113
  start-page: 3551
  year: 2016
  end-page: 3556
  ident: b36
  article-title: Discovery of fairy circles in Australia supports self-organization theory
  publication-title: Proc. Natl. Acad. Sci.
– volume: 85
  start-page: 1
  year: 2016
  end-page: 12
  ident: b47
  article-title: Mathematical modeling of population dynamics with Allee effect
  publication-title: Nonlinear Dynam.
– volume: 284
  start-page: 1826
  year: 1999
  end-page: 1828
  ident: b7
  article-title: Regular and irregular patterns in semiarid vegetation
  publication-title: Science
– volume: 181
  year: 2024
  ident: b43
  article-title: Pattern formation of a spatial vegetation system with cross-diffusion and nonlocal delay
  publication-title: Chaos Solitons Fractals
– volume: 300
  start-page: 1560
  year: 2003
  end-page: 1563
  ident: b12
  article-title: Climate-driven increases in global terrestrial net primary production from 1982 to 1999
  publication-title: Science
– volume: 73
  start-page: 1347
  year: 2013
  end-page: 1367
  ident: b28
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments V: the transition from patterns to desert
  publication-title: SIAM J. Appl. Math.
– volume: 148
  start-page: 1519
  year: 2022
  end-page: 1542
  ident: b32
  article-title: Bifurcation analysis of an extended Klausmeier–Gray–Scott model with infiltration delay
  publication-title: Stud. Appl. Math.
– volume: 85
  year: 2012
  ident: b46
  article-title: Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response
  publication-title: Phys. Rev. E— Stat. Nonlinear Soft Matter Phys.
– volume: 254
  start-page: 350
  year: 2008
  end-page: 360
  ident: b34
  article-title: Numerical investigation of spatial pattern in a vegetation model with feedback function
  publication-title: J. Theoret. Biol.
– volume: 467
  start-page: 3272
  year: 2011
  end-page: 3294
  ident: b25
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments II: patterns with the largest possible propagation speeds
  publication-title: Proc. R. Soc. A: Math. Phys. Eng. Sci.
– volume: 14
  start-page: 1307
  year: 2022
  ident: b14
  article-title: Data-driven artificial intelligence model of meteorological elements influence on vegetation coverage in North China
  publication-title: Remote. Sens.
– volume: 87
  year: 2001
  ident: b18
  article-title: Diversity of vegetation patterns and desertification
  publication-title: Phys. Rev. Lett.
– volume: 7
  start-page: 2544
  year: 2017
  ident: b39
  article-title: Analysis of soil water movement inside a footslope and a depression in a karst catchment, Southwest China
  publication-title: Sci. Rep.
– volume: 131
  year: 2024
  ident: b42
  article-title: Positive steady-state solutions for a vegetation–water model with saturated water absorption
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
– volume: 47
  start-page: RG1005
  year: 2009
  ident: b11
  article-title: Mathematical models of vegetation pattern formation in ecohydrology
  publication-title: Rev. Geophys.
– volume: 9
  year: 2014
  ident: b3
  article-title: Early warning signals of ecological transitions: methods for spatial patterns
  publication-title: PLoS One
– volume: 371
  year: 2013
  ident: b33
  article-title: Regime shifts in models of dryland vegetation
  publication-title: Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
– volume: 242
  start-page: 30
  year: 2013
  end-page: 41
  ident: b26
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments III: the transition between homoclinic solutions
  publication-title: Phys. D: Nonlinear Phenom.
– volume: 74
  start-page: 803
  year: 2012
  end-page: 833
  ident: b20
  article-title: A nonlinear stability analysis of vegetative Turing pattern formation for an interaction–diffusion plant-surface water model system in an arid flat environment
  publication-title: Bull. Math. Biol.
– volume: 121
  year: 2024
  ident: b6
  article-title: Self-organization as a mechanism of resilience in dryland ecosystems
  publication-title: Proc. Natl. Acad. Sci.
– volume: 61
  start-page: 200
  year: 2018
  end-page: 215
  ident: b35
  article-title: Effects of feedback regulation on vegetation patterns in semi-arid environments
  publication-title: Appl. Math. Model.
– volume: 6
  start-page: 166
  year: 2016
  end-page: 171
  ident: b1
  article-title: Accelerated dryland expansion under climate change
  publication-title: Nat. Clim. Chang.
– volume: 181
  year: 2019
  ident: b38
  article-title: Using water isotopes to analyze water uptake during vegetation succession on abandoned cropland on the Loess Plateau, China
  publication-title: Catena
– volume: 82
  start-page: 50
  year: 2001
  end-page: 61
  ident: b9
  article-title: Vegetation pattern formation in semi-arid grazing systems
  publication-title: Ecology
– volume: 6
  start-page: 163
  year: 2011
  end-page: 187
  ident: b15
  article-title: Modeling dryland landscapes
  publication-title: Math. Model. Nat. Phenom.
– volume: 38
  start-page: 586
  year: 2021
  end-page: 600
  ident: b40
  article-title: Pattern dynamics of vegetation system with Holling-type II and nonlocal delay
  publication-title: Chin. J. Eng. Math.
– volume: 74
  start-page: 332
  year: 2008
  end-page: 344
  ident: b30
  article-title: Vegetation pattern shift as a result of rising atmospheric CO2 in arid ecosystems
  publication-title: Theor. Popul. Biol.
– volume: 98
  start-page: 261
  year: 2004
  end-page: 271
  ident: b45
  article-title: Vegetation spots and stripes: dissipative structures in arid landscapes
  publication-title: Int. J. Quantum Chem.
– volume: 7
  start-page: 417
  year: 2017
  end-page: 422
  ident: b2
  article-title: Drylands face potential threat under 2°C global warming target
  publication-title: Nat. Clim. Chang.
– volume: 85
  start-page: 50
  year: 2022
  ident: b44
  article-title: Spatial dynamics of a vegetation model with uptake–diffusion feedback in an arid environment
  publication-title: J. Math. Biol.
– volume: 120
  year: 2023
  ident: b5
  article-title: The hidden order of Turing patterns in arid and semi-arid vegetation ecosystems
  publication-title: Proc. Natl. Acad. Sci.
– volume: vol. 10
  year: 2015
  ident: b16
  publication-title: Nonlinear Physics of Ecosystems
– volume: 85
  start-page: 50
  issue: 5
  year: 2022
  ident: 10.1016/j.physa.2025.130676_b44
  article-title: Spatial dynamics of a vegetation model with uptake–diffusion feedback in an arid environment
  publication-title: J. Math. Biol.
  doi: 10.1007/s00285-022-01825-0
– volume: 6
  start-page: 163
  issue: 1
  year: 2011
  ident: 10.1016/j.physa.2025.130676_b15
  article-title: Modeling dryland landscapes
  publication-title: Math. Model. Nat. Phenom.
  doi: 10.1051/mmnp/20116109
– volume: 74
  start-page: 332
  issue: 4
  year: 2008
  ident: 10.1016/j.physa.2025.130676_b30
  article-title: Vegetation pattern shift as a result of rising atmospheric CO2 in arid ecosystems
  publication-title: Theor. Popul. Biol.
  doi: 10.1016/j.tpb.2008.09.004
– volume: 300
  start-page: 1560
  issue: 5625
  year: 2003
  ident: 10.1016/j.physa.2025.130676_b12
  article-title: Climate-driven increases in global terrestrial net primary production from 1982 to 1999
  publication-title: Science
  doi: 10.1126/science.1082750
– volume: 284
  start-page: 1826
  issue: 5421
  year: 1999
  ident: 10.1016/j.physa.2025.130676_b7
  article-title: Regular and irregular patterns in semiarid vegetation
  publication-title: Science
  doi: 10.1126/science.284.5421.1826
– volume: 244
  start-page: 680
  issue: 4
  year: 2007
  ident: 10.1016/j.physa.2025.130676_b10
  article-title: A mathematical model of plants as ecosystem engineers
  publication-title: J. Theoret. Biol.
  doi: 10.1016/j.jtbi.2006.08.006
– volume: 254
  start-page: 350
  issue: 2
  year: 2008
  ident: 10.1016/j.physa.2025.130676_b34
  article-title: Numerical investigation of spatial pattern in a vegetation model with feedback function
  publication-title: J. Theoret. Biol.
  doi: 10.1016/j.jtbi.2008.05.017
– volume: 38
  start-page: 586
  issue: 04
  year: 2021
  ident: 10.1016/j.physa.2025.130676_b40
  article-title: Pattern dynamics of vegetation system with Holling-type II and nonlocal delay
  publication-title: Chin. J. Eng. Math.
– volume: 23
  start-page: 2657
  issue: 10
  year: 2010
  ident: 10.1016/j.physa.2025.130676_b24
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments I
  publication-title: Nonlinearity
  doi: 10.1088/0951-7715/23/10/016
– volume: 98
  start-page: 261
  issue: 2
  year: 2004
  ident: 10.1016/j.physa.2025.130676_b45
  article-title: Vegetation spots and stripes: dissipative structures in arid landscapes
  publication-title: Int. J. Quantum Chem.
  doi: 10.1002/qua.10878
– volume: 74
  start-page: 803
  year: 2012
  ident: 10.1016/j.physa.2025.130676_b20
  article-title: A nonlinear stability analysis of vegetative Turing pattern formation for an interaction–diffusion plant-surface water model system in an arid flat environment
  publication-title: Bull. Math. Biol.
  doi: 10.1007/s11538-011-9688-7
– volume: 73
  start-page: 330
  issue: 1
  year: 2013
  ident: 10.1016/j.physa.2025.130676_b27
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments IV: slowly moving patterns and their stability
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/120862648
– volume: 467
  start-page: 3272
  issue: 2135
  year: 2011
  ident: 10.1016/j.physa.2025.130676_b25
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments II: patterns with the largest possible propagation speeds
  publication-title: Proc. R. Soc. A: Math. Phys. Eng. Sci.
  doi: 10.1098/rspa.2011.0194
– volume: 59
  start-page: 263
  year: 1997
  ident: 10.1016/j.physa.2025.130676_b22
  article-title: On the origin of tiger bush
  publication-title: Bull. Math. Biol.
  doi: 10.1007/BF02462004
– volume: 121
  issue: 6
  year: 2024
  ident: 10.1016/j.physa.2025.130676_b6
  article-title: Self-organization as a mechanism of resilience in dryland ecosystems
  publication-title: Proc. Natl. Acad. Sci.
  doi: 10.1073/pnas.2305153121
– volume: 7
  start-page: 417
  issue: 6
  year: 2017
  ident: 10.1016/j.physa.2025.130676_b2
  article-title: Drylands face potential threat under 2°C global warming target
  publication-title: Nat. Clim. Chang.
  doi: 10.1038/nclimate3275
– volume: 112
  start-page: 8675
  issue: 10
  year: 2024
  ident: 10.1016/j.physa.2025.130676_b31
  article-title: Effects of climate change on vegetation pattern in Baotou, China
  publication-title: Nonlinear Dynam.
  doi: 10.1007/s11071-024-09500-3
– volume: 82
  start-page: 50
  issue: 1
  year: 2001
  ident: 10.1016/j.physa.2025.130676_b9
  article-title: Vegetation pattern formation in semi-arid grazing systems
  publication-title: Ecology
  doi: 10.1890/0012-9658(2001)082[0050:VPFISA]2.0.CO;2
– volume: 48
  start-page: 3190
  issue: 3
  year: 2025
  ident: 10.1016/j.physa.2025.130676_b19
  article-title: Pattern dynamics in a water–vegetation model with cross-diffusion and nonlocal delay
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.10480
– volume: 374
  start-page: eabj0359
  issue: 6564
  year: 2021
  ident: 10.1016/j.physa.2025.130676_b4
  article-title: Evasion of tipping in complex systems through spatial pattern formation
  publication-title: Science
  doi: 10.1126/science.abj0359
– volume: 72
  start-page: 30
  issue: 11
  year: 2019
  ident: 10.1016/j.physa.2025.130676_b17
  article-title: Vegetation pattern formation: The mechanisms behind the forms
  publication-title: Phys. Today
  doi: 10.1063/PT.3.4340
– volume: 242
  start-page: 30
  issue: 1
  year: 2013
  ident: 10.1016/j.physa.2025.130676_b26
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments III: the transition between homoclinic solutions
  publication-title: Phys. D: Nonlinear Phenom.
  doi: 10.1016/j.physd.2012.08.014
– volume: 85
  start-page: 1
  year: 2016
  ident: 10.1016/j.physa.2025.130676_b47
  article-title: Mathematical modeling of population dynamics with Allee effect
  publication-title: Nonlinear Dynam.
  doi: 10.1007/s11071-016-2671-y
– volume: 113
  start-page: 3551
  issue: 13
  year: 2016
  ident: 10.1016/j.physa.2025.130676_b36
  article-title: Discovery of fairy circles in Australia supports self-organization theory
  publication-title: Proc. Natl. Acad. Sci.
  doi: 10.1073/pnas.1522130113
– volume: 91
  start-page: 249
  year: 2018
  ident: 10.1016/j.physa.2025.130676_b37
  article-title: Water utilization characteristics of typical vegetation in the rocky mountain area of Beijing, China
  publication-title: Ecol. Indic.
  doi: 10.1016/j.ecolind.2018.03.083
– volume: 14
  start-page: 1307
  issue: 6
  year: 2022
  ident: 10.1016/j.physa.2025.130676_b14
  article-title: Data-driven artificial intelligence model of meteorological elements influence on vegetation coverage in North China
  publication-title: Remote. Sens.
  doi: 10.3390/rs14061307
– volume: 23
  start-page: 39
  year: 2013
  ident: 10.1016/j.physa.2025.130676_b29
  article-title: Rise and fall of periodic patterns for a generalized Klausmeier–Gray–Scott model
  publication-title: J. Nonlinear Sci.
  doi: 10.1007/s00332-012-9139-0
– volume: 6
  start-page: 166
  issue: 2
  year: 2016
  ident: 10.1016/j.physa.2025.130676_b1
  article-title: Accelerated dryland expansion under climate change
  publication-title: Nat. Clim. Chang.
  doi: 10.1038/nclimate2837
– volume: 7
  start-page: 2544
  issue: 1
  year: 2017
  ident: 10.1016/j.physa.2025.130676_b39
  article-title: Analysis of soil water movement inside a footslope and a depression in a karst catchment, Southwest China
  publication-title: Sci. Rep.
  doi: 10.1038/s41598-017-02619-x
– volume: 43
  start-page: 239
  year: 2022
  ident: 10.1016/j.physa.2025.130676_b8
  article-title: Impacts of climate change on vegetation pattern: Mathematical modeling and data analysis
  publication-title: Phys. Life Rev.
  doi: 10.1016/j.plrev.2022.09.005
– volume: 14
  start-page: 473
  issue: 1
  year: 2024
  ident: 10.1016/j.physa.2025.130676_b21
  article-title: Effect of nonlocal delay with strong kernel on vegetation pattern
  publication-title: J. Appl. Anal. Comput.
– volume: 148
  start-page: 1519
  issue: 4
  year: 2022
  ident: 10.1016/j.physa.2025.130676_b32
  article-title: Bifurcation analysis of an extended Klausmeier–Gray–Scott model with infiltration delay
  publication-title: Stud. Appl. Math.
  doi: 10.1111/sapm.12482
– volume: 131
  year: 2024
  ident: 10.1016/j.physa.2025.130676_b42
  article-title: Positive steady-state solutions for a vegetation–water model with saturated water absorption
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2023.107802
– volume: vol. 10
  year: 2015
  ident: 10.1016/j.physa.2025.130676_b16
– volume: 371
  issue: 2004
  year: 2013
  ident: 10.1016/j.physa.2025.130676_b33
  article-title: Regime shifts in models of dryland vegetation
  publication-title: Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
  doi: 10.1098/rsta.2012.0358
– volume: 181
  year: 2019
  ident: 10.1016/j.physa.2025.130676_b38
  article-title: Using water isotopes to analyze water uptake during vegetation succession on abandoned cropland on the Loess Plateau, China
  publication-title: Catena
  doi: 10.1016/j.catena.2019.104095
– volume: 85
  issue: 2
  year: 2012
  ident: 10.1016/j.physa.2025.130676_b46
  article-title: Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response
  publication-title: Phys. Rev. E— Stat. Nonlinear Soft Matter Phys.
  doi: 10.1103/PhysRevE.85.021924
– volume: 120
  issue: 42
  year: 2023
  ident: 10.1016/j.physa.2025.130676_b5
  article-title: The hidden order of Turing patterns in arid and semi-arid vegetation ecosystems
  publication-title: Proc. Natl. Acad. Sci.
  doi: 10.1073/pnas.2306514120
– volume: 47
  start-page: RG1005
  issue: 1
  year: 2009
  ident: 10.1016/j.physa.2025.130676_b11
  article-title: Mathematical models of vegetation pattern formation in ecohydrology
  publication-title: Rev. Geophys.
  doi: 10.1029/2007RG000256
– volume: 12
  start-page: 30
  year: 1972
  ident: 10.1016/j.physa.2025.130676_b23
  article-title: A theory of biological pattern formation
  publication-title: Kybernetik
  doi: 10.1007/BF00289234
– volume: 87
  issue: 19
  year: 2001
  ident: 10.1016/j.physa.2025.130676_b18
  article-title: Diversity of vegetation patterns and desertification
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.87.198101
– volume: 73
  start-page: 1347
  issue: 4
  year: 2013
  ident: 10.1016/j.physa.2025.130676_b28
  article-title: Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments V: the transition from patterns to desert
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/120899510
– volume: 181
  year: 2024
  ident: 10.1016/j.physa.2025.130676_b43
  article-title: Pattern formation of a spatial vegetation system with cross-diffusion and nonlocal delay
  publication-title: Chaos Solitons Fractals
  doi: 10.1016/j.chaos.2024.114622
– volume: 249
  start-page: 198
  year: 2018
  ident: 10.1016/j.physa.2025.130676_b13
  article-title: Changes in global vegetation activity and its driving factors during 1982–2013
  publication-title: Agricult. Forest. Meterol.
  doi: 10.1016/j.agrformet.2017.11.013
– volume: 9
  year: 2021
  ident: 10.1016/j.physa.2025.130676_b41
  article-title: Pattern dynamics of vegetation growth with saturated water absorption
  publication-title: Front. Phys.
  doi: 10.3389/fphy.2021.721115
– volume: 61
  start-page: 200
  year: 2018
  ident: 10.1016/j.physa.2025.130676_b35
  article-title: Effects of feedback regulation on vegetation patterns in semi-arid environments
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2018.04.010
– volume: 9
  issue: 3
  year: 2014
  ident: 10.1016/j.physa.2025.130676_b3
  article-title: Early warning signals of ecological transitions: methods for spatial patterns
  publication-title: PLoS One
  doi: 10.1371/journal.pone.0092097
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Snippet Desertification represents one of the most pressing ecological challenges globally, where vegetation patterns serve as critical indicators of ecosystem...
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StartPage 130676
SubjectTerms Bifurcation phenomena
Multi-scale analysis
Saturation water absorption effect
Soil water diffusion feedback
Vegetation patterns
Title Pattern dynamics of a vegetation-water model with saturated effect and diffusion feedback
URI https://dx.doi.org/10.1016/j.physa.2025.130676
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