  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
pattern-forming 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 gap solutions close to a homogeneous
instability. Additionally, we numerically solve the vegetation model and use
continuation methods to study the bifurcation structure and radial stability of
localised radial spots and gaps. We conclude by investigating the effect of
varying certain parameter values on the existence and stability of these
localised radial patterns.
