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Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments
Jonathan A Sherratt1, Gabriel J Lord
1Department of Mathematics and Maxwell Institute, Heriot-Watt University, Edinburgh EH14 4AS, UK. jas@macs.hw.ac.uk
Theoretical Population Biology
|November 1, 2006
Summary
Vegetation stripes in semi-arid regions form due to water competition. This study reveals patterns exist at lower rainfall levels than previously thought, with selection depending on rainfall history.
Area of Science:
- Ecology
- Mathematical Biology
- Hydrology
Background:
- Semi-arid environments often exhibit self-organized vegetation patterns, notably stripes on gentle slopes.
- Previous models, like Klausmeier's, suggest water competition drives these spatial patterns.
Purpose of the Study:
- To conduct a detailed numerical bifurcation analysis of vegetation stripe patterns in a full nonlinear model.
- To investigate pattern formation across a wider range of rainfall levels and explore mode selection mechanisms.
Main Methods:
- Numerical bifurcation analysis of pattern ordinary differential equations (ODEs) and partial differential equations (PDEs).
- Exploration of model solutions under varying rainfall conditions and initial states.
Main Results:
- Vegetation stripe patterns are shown to exist for a broad spectrum of rainfall, including significantly lower levels than previously considered.
- Multiple stable pattern wavelengths were identified for many rainfall levels, with selection contingent on initial conditions.
- Hysteresis in pattern selection was observed, influenced by rainfall history.
Conclusions:
- The model supports vegetation stripe formation under diverse rainfall regimes, expanding the understanding of arid ecosystem dynamics.
- Initial conditions and rainfall history play a crucial role in determining stable vegetation pattern selection, highlighting potential for hysteresis.
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