  We study the time evolution of spherical, excited ($i.e.$ nodeful) boson star
models. We consider a model including quartic self-interactions, controlled by
a coupling $\Lambda$. Performing non-linear simulations of the
Einstein-(complex)-Klein-Gordon system, using as initial data equilibrium boson
stars solutions of that system, we assess the impact of $\Lambda$ in the
stability properties of the boson stars. In the absence of self-interactions
($\Lambda=0$), we observe the known behaviour that the excited stars in the
(candidate) stable branch decay to a non-excited star without a node; however,
we show that for large enough values of the self-interactions coupling, these
excited stars do not decay (up to timescales of about $t\sim 10^4$). The
stabilization of the excited states for large enough self-interactions is
further supported by evidence that the nodeful states dynamically form through
the gravitational cooling mechanism, starting from dilute initial data. Our
results support the healing power (against dynamical instabilities) of
self-interactions, recently unveiled in the context of the non-axisymmetric
instabilities of spinning boson stars.
