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math.DS2024
The role of spatial dimension in the emergence of localised radial patterns from a Turing instability
Dan J. Hill
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We pro…
math.DS2024
Radial amplitude equations for fully localised planar patterns
Dan J. Hill, David J. B. Lloyd
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, th…
math.DS2023
Predicting the emergence of localised dihedral patterns in models for dryland vegetation
Dan J. Hill
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'…