Multistability shifts in an aird vegetation system with nonlocal water absorption effect

Area of Science:

• Ecological modeling
• Mathematical biology
• Arid ecosystem dynamics

Background:

• Vegetation patterns in arid regions are often periodic, typically described by Turing patterns.
• Previous models overlooked vegetation's ability to absorb water nonlocally.
• Understanding these patterns is crucial for arid land management.

Purpose of the Study:

• To develop a vegetation-water model incorporating nonlocal water absorption.
• To analyze the conditions for Turing bifurcation and pattern formation.
• To investigate the impact of nonlocal effects on multistability and pattern diversity.

Main Methods:

• Development of a vegetation-water model with nonlocal absorption.
• Application of weakly nonlinear analysis to derive amplitude equations.
• Analysis of Turing bifurcation conditions and stability states.

Main Results:

• Nonlocal absorption can induce supercritical Turing bifurcation, unlike subcritical types in previous models.
• The nonlocal effect drives transitions between supercritical and subcritical Turing bifurcations.
• Multistability states, including tristability (bare soil, uniform, and periodic vegetation), emerge.
• Observed patterns in Senegal are explained, differing from Australian fairy circles.
• Vegetation systems shift from monostability to bistability and tristability with changing precipitation.

Conclusions:

• Nonlocal water absorption significantly impacts vegetation pattern formation and ecosystem stability.
• The model explains diverse arid vegetation patterns and their transitions.
• Findings provide new insights into arid ecosystem dynamics and management strategies.