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Related Experiment Video

Updated: Apr 1, 2026

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Localised pattern formation in a model for dryland vegetation.

J H P Dawes1, J L M Williams2

  • 1Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK. J.H.P.Dawes@bath.ac.uk.

Journal of Mathematical Biology
|October 12, 2015
PubMed
Summary
This summary is machine-generated.

This study analyzes a vegetation growth model in semi-arid landscapes, revealing how precipitation changes lead to transitions from bare ground to vegetation patches, periodic patterns, and uniform vegetation cover.

Keywords:
BifurcationHomoclinic snakingLocalised stateSemi-arid environment

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Area of Science:

  • Ecological modeling
  • Mathematical biology
  • Pattern formation

Background:

  • Vegetation patterns in semi-arid regions are crucial for ecosystem stability.
  • Previous models, like Klausmeier's, simplified vegetation dynamics.
  • The von Hardenberg model incorporates additional physical effects for a more comprehensive analysis.

Purpose of the Study:

  • To analyze the von Hardenberg model for vegetation growth in semi-arid landscapes.
  • To investigate pattern formation and bifurcations in a reduced model under specific conditions.
  • To understand the transitions between different vegetation states as precipitation varies.

Main Methods:

  • Analysis of a partial differential equation model describing soil water and vegetation.
  • Reduction of the system to a parabolic-elliptic system by assuming fast water diffusion.
  • Weakly nonlinear analysis to study instabilities, bifurcations, and pattern formation.

Main Results:

  • Pattern-forming instabilities are predominantly subcritical.
  • Localized vegetation solutions are organized by homoclinic snaking curves.
  • The model predicts a sequence of transitions: bare state -> localized patches -> periodic patterns -> uniform vegetation with increasing precipitation.

Conclusions:

  • The von Hardenberg model captures complex vegetation dynamics in semi-arid environments.
  • Hysteresis is a key feature in the transitions between vegetation states.
  • The model's findings are consistent with known pattern-forming system behaviors.