• Corpus ID: 236447362

Existence of localised radial patterns in a model for dryland vegetation

@inproceedings{Hill2021ExistenceOL,
  title={Existence of localised radial patterns in a model for dryland vegetation},
  author={Daniel J. Hill},
  year={2021}
}
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of ‘fairy circles’. We consider stationary localised radial solutions to a reduced model for dryland vegetation on flat terrain. By considering certain prototypical patternforming systems, we prove the existence of three classes of localised radial patterns bifurcating from a Turing instability. We also present evidence for the existence of localised… 

Large amplitude radially symmetric spots and gaps in a dryland ecosystem model

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References

SHOWING 1-10 OF 60 REFERENCES

Localised pattern formation in a model for dryland vegetation

The von Hardenberg model displays a sequence of (often hysteretic) transitions from a non-vegetated state, to localised patches of vegetation that exist with uniform low-level vegetation, to periodic patterns, to higher-level uniform vegetation as the precipitation parameter increases.

Mathematical models of vegetation pattern formation in ecohydrology

Highly organized vegetation patterns can be found in a number of landscapes around the world. In recent years, several authors have investigated the processes underlying vegetation pattern formation.

Regular and irregular patterns in semiarid vegetation

A simple model of plant and water dynamics based on ecologically realistic assumptions and with reasonable parameter values captures both the regular and irregular patterns of vegetation in semiarid regions.

Localized structures in dryland vegetation: forms and functions.

The various biomass-water structures are expected to function differently in the context of a plant community, forming landscapes of varying species diversity.

On the repulsive interaction between localised vegetation patches in scarce environments

It is shown analytically and numerically that the interaction between two or more patches is always repulsive, and only a single localised vegetation patch is stable, and other localised bounded states or clusters of them are unstable.

Assessing the robustness of spatial pattern sequences in a dryland vegetation model

It is found that a quantity calculated via bifurcation-theoretic analysis appears to serve as a proxy for the pattern sequences that occur in numerical simulations across a range of parameter values, suggesting that the standard sequence is a robust prediction of the model.

Vegetation patterns along a rainfall gradient

Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems

In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. We

Self-Replication of Localized Vegetation Patches in Scarce Environments

A robust phenomena observed in semi-arid ecosystems, by which localized vegetation patches split in a process called self-replication is studied, which is opposite to the desertification since it allows to repopulate territories devoid of vegetation.
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