  By deriving a three dimensional vector set of Maxwell-Bloch equations, we
report on an ab-initio investigation of a spherical Mie nanolaser. Parallel
numerical simulations predict a rich physical scenario, ranging from a
nontrivial vectorial energy-matter interplay in the initial stage of evolution
to mode competition and dynamical frequency pulling effects. Application of
these effects could favor the realization of nonlinearly-controlled
largely-tunable nanolaser devices.
