  We report the mean field model of nonequilibrium polariton condensation in
annular effective non-Hermitian potential traps, stemming from incoherent
optically induced excitonic reservoirs of annular shape. We solve the
linearized extended Gross-Pitaevskii equation in the approximation of two
delta-function effective shell potentials for complex spectra of trapped
polariton modes and calculate corresponding condensation threshold optical
pumping powers. The exhaustive map of condensate quantum number transitions in
the multi-dimensional space of trap parameters, including a cascade of
topological charge increments, is drastically different from the single annular
trap case in topology and the range of accessible condensate states.
