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<p>Self-organized vegetation patterns, such as regular bands, spots and gaps, have been observed in arid and semi-arid regions, banded vegetation is particularly associated with sloped terrains. In this paper, we consider a vegetation-water model in a semi-arid hillsides environment using reaction diffusion system couples the plant biomass and infiltrated water, to investigate the banded vegetation pattern formation. Conditions on the Hopf bifurcation and the Turing instability are established. Firstly, for the ordinary differential equations, the existence and stability of the bifurcating periodic solutions at the non-trivial equilibrium are derived. Then for the reaction–diffusion equations with zero-flux boundary conditions, Turing instability area dependent on the diffusion coefficient is obtained. To study the dynamics behaviors near the Turing bifurcation, the weakly non-linear analysis technique is applied to obtain the amplitude equations. Finally, theoretical results are verified through numerical simulations, and the environmental factor driving the emergence of banded vegetation pattern has been identified.</p>

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The influence of infiltrated water diffusion on the formation of banded vegetation pattern on hill slopes of semi-arid environments

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Souhail Roman,
  • Radouane Yafia,
  • M. A. Aziz Alaoui

摘要

Self-organized vegetation patterns, such as regular bands, spots and gaps, have been observed in arid and semi-arid regions, banded vegetation is particularly associated with sloped terrains. In this paper, we consider a vegetation-water model in a semi-arid hillsides environment using reaction diffusion system couples the plant biomass and infiltrated water, to investigate the banded vegetation pattern formation. Conditions on the Hopf bifurcation and the Turing instability are established. Firstly, for the ordinary differential equations, the existence and stability of the bifurcating periodic solutions at the non-trivial equilibrium are derived. Then for the reaction–diffusion equations with zero-flux boundary conditions, Turing instability area dependent on the diffusion coefficient is obtained. To study the dynamics behaviors near the Turing bifurcation, the weakly non-linear analysis technique is applied to obtain the amplitude equations. Finally, theoretical results are verified through numerical simulations, and the environmental factor driving the emergence of banded vegetation pattern has been identified.