IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v241y2026ipap689-703.html

Vegetation-water system with positive feedback: Effects of local versus nonlocal grazing

Author

Listed:
  • Li, Nishan
  • Wu, Daiyong
  • Zhang, Zidie
  • Ye, Luhong

Abstract

Positive feedback plays a crucial role in maintaining ecosystem stability and preventing desertification in semi-arid regions. However, researches on the evaporation suppression as part of this positive feedback remain limited. To deeply explore the influence of positive feedback effect on the stability of positive equilibrium point in local and nonlocal grazing systems, we propose and investigate a nonlocal grazing vegetation water model system with saturated evaporation suppression effect and soil water diffusion intensity. The eigenvalue method is used to analyze the stability of the positive equilibrium point, and different parameters are controlled to analyze the influence on the stability of the positive equilibrium point in the local and nonlocal systems. Our results show that in the absence of evaporation suppression, overgrazing may lead to the disappearance of positive equilibrium points, indicating desertification in semi-arid regions. In the presence of evaporation suppression, the grazing intensity beyond a certain threshold may destabilize the system, resulting in Hopf bifurcations. Moreover, inhomogeneous Hopf bifurcations do not occur under the nonlocal grazing. Furthermore, we obtain that the positive feedback effect with soil water diffusion affects the stability of positive equilibrium points and leads to the occurrence of Turing instability. Note that the range of the intensity of soil water diffusion that causes Turing instability becomes small for the nonlocal grazing system. Numerical simulations reveal that the nonlocal grazing is more conducive to the growth and survival of vegetation compared to the local grazing.

Suggested Citation

  • Li, Nishan & Wu, Daiyong & Zhang, Zidie & Ye, Luhong, 2026. "Vegetation-water system with positive feedback: Effects of local versus nonlocal grazing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 689-703.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:689-703
    DOI: 10.1016/j.matcom.2025.09.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542500391X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.09.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Xuebing & An, Qi & Moussaoui, Ali, 2025. "Effect of density-dependent diffusion on a diffusive predator–prey model in spatially heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 1-18.
    2. Ding, Linglong & Zhang, Xuebing & Lv, Guangying, 2024. "Dynamics of a plankton community with delay and herd-taxis," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Zhang, Zidie & Wu, Daiyong & Li, Nishan, 2024. "Predator invasion in a spatially heterogeneous predator-prey model with group defense and prey-taxis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 270-282.
    4. Guo, Gaihui & Qin, Qijing & Cao, Hui & Jia, Yunfeng & Pang, Danfeng, 2024. "Pattern formation of a spatial vegetation system with cross-diffusion and nonlocal delay," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
    6. Liang, Juan & Liu, Chen & Sun, Gui-Quan & Li, Li & Zhang, Lai & Hou, Meiting & Wang, Hao & Wang, Zhen, 2022. "Nonlocal interactions between vegetation induce spatial patterning," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guo, Gaihui & Qin, Qijing & Cao, Hui & Jia, Yunfeng & Pang, Danfeng, 2024. "Pattern formation of a spatial vegetation system with cross-diffusion and nonlocal delay," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Yang, Yafei & Zhao, Xin & Fan, Meng, 2026. "Modeling the impact of Allee effect, herd behavior and harvesting on kelp beds: A cross-diffusion-ODE dynamical approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 525-554.
    3. Shi, Yu & Luo, Xiao-Feng & Zhang, Yong-Xin & Sun, Gui-Quan, 2023. "An indicator of Crohn’s disease severity based on Turing patterns," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Consolo, Giancarlo & Curró, Carmela & Grifó, Gabriele & Valenti, Giovanna, 2024. "Stationary and Oscillatory patterned solutions in three-compartment reaction–diffusion systems: Theory and application to dryland ecology," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    5. Yuan, Xiaoyue & Zhang, Xuebing & Liu, Wenjun & Moussaoui, Ali & Auger, Pierre, 2025. "Global dynamics of a chemotaxis system with toxicity in invasive species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 235(C), pages 16-36.
    6. Zhang, Xuebing & Wu, Bin, 2025. "Dynamics of a diffusion-advection model with local perception of toxins," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    7. Wang, Fatao & Yang, Ruizhi & Zhang, Xin, 2024. "Turing patterns in a predator–prey model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 170-191.
    8. Wenxu Ning & Zhijun Liu & Lianwen Wang & Ronghua Tan, 2021. "Analysis of a Stochastic Competitive Model with Saturation Effect and Distributed Delay," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1435-1459, December.
    9. Lv, Zunyou & Maimaiti, Yimamu, 2026. "Spatiotemporal evolution and predictive analysis of vegetation patterns in the Bayanbulak Grassland under climate change," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    10. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    11. Zhi, Shun & Bai, Dingyong & Su, Youhui, 2026. "Turing patterns induced by cross-diffusion in a predator-prey model with Smith-type prey growth and additive predation effects," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    12. Bai, Huimin & Fan, Yu-Xuan & Li, Li, 2025. "Pattern dynamics of a vegetation-water model with saturated effect and diffusion feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 673(C).
    13. Han, Bingtao & Jiang, Daqing, 2022. "Stationary distribution, extinction and density function of a stochastic prey-predator system with general anti-predator behavior and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Ren, Yonghui & Wu, Peng, 2025. "Complete threshold dynamics of a reaction–diffusion schistosomiasis model in different time-evolving domains," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    15. Sarfaraz, Wakil & Yigit, Gulsemay & Barreira, Raquel & Remaki, Lakhdar & Alhazmi, Muflih & Madzvamuse, Anotida, 2024. "Understanding the dual effects of linear cross-diffusion and geometry on reaction–diffusion systems for pattern formation," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    16. Zhang, Hao Lu & Wang, Yu Lan & Bi, Jun Xi & Bao, Shu Hong, 2026. "Novel pattern dynamics in a vegetation-water reaction–diffusion model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 97-116.
    17. Wang, Fatao & Yang, Ruizhi, 2023. "Spatial pattern formation driven by the cross-diffusion in a predator–prey model with Holling type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    18. Chen, Mengxin & Wu, Ranchao, 2023. "Steady states and spatiotemporal evolution of a diffusive predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    19. Zhu, Linhe & Tang, Yuxuan & Shen, Shuling, 2023. "Pattern study and parameter identification of a reaction-diffusion rumor propagation system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    20. Li, Chunru & Yuan, Xuesong & Gong, Yu, 2025. "Dynamic analysis of a Solow–Swan model with capital-induced labor migration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 73-85.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:689-703. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.