 Bifurcation analysis of a spatial vegetation modelHong-Tao Zhang, Yong-Ping Wu, Gui-Quan Sun, Chen Liu and Guo-Lin Feng Applied Mathematics and Computation, 2022, vol. 434, issue C 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. Keywords: Cross-diffusion; Steady-state bifurcation; Non-constant solutions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322005331 DOI: 10.1016/j.amc.2022.127459 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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