  The temporal evolution of entanglement between a noisy system and an
ancillary system is analyzed in the context of continuous time open quantum
system dynamics. Focusing on a couple of analytically solvable models for qubit
systems, we study how Markovian and non-Markovian characteristics influence the
problem, discussing in particular their associated entanglement-breaking
regimes. These performances are compared with those one could achieve when the
environment of the system is forced to return to its input configuration via
periodic instantaneous resetting procedures.
