  We give the map representing the evolution of a qubit under the action of
non-dissipative random external fields. From this map we construct the
corresponding master equation that in turn allows us to phenomenologically
introduce population damping of the qubit system. We then compare, in this
system, the time-regions when non-Markovianity is present on the basis of
different criteria both for the non-dissipative and dissipative case. We show
that the adopted criteria agree both in the non-dissipative case and in the
presence of population damping.
