  The recent discovery of an Earth-like exoplanet around Proxima Centauri has
shined a spot light on slowly rotating fully convective M-stars. When such
stars rotate rapidly (period $\lesssim 20$ days), they are known to generate
very high levels of activity that is powered by a magnetic field much stronger
than the solar magnetic field. Recent theoretical efforts are beginning to
understand the dynamo process that generates such strong magnetic fields.
However, the observational and theoretical landscape remains relatively
uncharted for fully convective M-stars that rotate slowly. Here we present an
anelastic dynamo simulation designed to mimic some of the physical
characteristics of Proxima Centauri, a representative case for slowly rotating
fully convective M-stars. The rotating convection spontaneously generates
differential rotation in the convection zone which drives coherent magnetic
cycles where the axisymmetric magnetic field repeatedly changes polarity at all
latitudes as time progress. The typical length of the `activity' cycle in the
simulation is about nine years, in good agreement with the recently proposed
activity cycle length of about seven years for Proxima Centauri. Comparing our
results with earlier work, we hypothesis that the dynamo mechanism undergoes a
fundamental change in nature as fully convective stars spin down with age.
