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Localised patterns are often observed in models for dryland vegetation, bothas peaks of vegetation in a desert state and as gaps within a vegetated state,known as `fairy circles'. Recent results from radial spatial dynamics show thatapproximations of localised patterns with dihedral symmetry emerge from aTuring instability in general reaction--diffusion systems, which we apply toseveral vegetation models. We present a systematic guide for finding suchpatterns in a given reaction--diffusion model, during which we obtain four keyquantities that allow us to predict the qualitative properties of our solutionswith minimal analysis. Our results are complemented by numerical simulationsfor various localised states in four well-established vegetation models,highlighting the universality of such solutions.

Predicting the emergence of localised dihedral patterns in models for dryland vegetation