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Bifurcation analysis of a spatial vegetation model

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  • Zhang, Hong-Tao
  • Wu, Yong-Ping
  • Sun, Gui-Quan
  • Liu, Chen
  • Feng, Guo-Lin

Abstract

Vegetation pattern can describe spatial feature of vegetation in arid ecosystem. Soil-water diffusion is of vital importance in spatial structures of vegetation, which is not comprehensively understood. In this thesis, we reveal the impact of soil-water diffusion on vegetation patterns through steady-state bifurcation analysis. The result indicates that if soil-water diffusion coefficient is appropriately large, there is at least one non-constant steady-state solution to a spatial vegetation system. Moreover, with the aid of Crandall-Rabinowitz bifurcation theorem and implicit function theorem, local structure of non-constant steady-state solutions is obtained. Subsequently, the global continuation of the local steady-state bifurcation is performed, and we get global structure of non-constant solution. At last, the above non-constant steady-state solution is illustrated by our numerical simulations. The extended simulation additionally shows that the spatial heterogeneity of species is enhanced gradually as soil-water diffusion increases.

Suggested Citation

  • Zhang, Hong-Tao & Wu, Yong-Ping & Sun, Gui-Quan & Liu, Chen & Feng, Guo-Lin, 2022. "Bifurcation analysis of a spatial vegetation model," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    • Handle: RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322005331
    DOI: 10.1016/j.amc.2022.127459
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    References listed on IDEAS

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    1. Liu, Chen & Li, Li & Wang, Zhen & Wang, Ruiwu, 2019. "Pattern transitions in a vegetation system with cross-diffusion," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 255-262.
    2. Xue, Qiang & Liu, Chen & Li, Li & Sun, Gui-Quan & Wang, Zhen, 2021. "Interactions of diffusion and nonlocal delay give rise to vegetation patterns in semi-arid environments," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    3. 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.
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