  For many open quantum systems, a master equation approach employing the
Markov approximation cannot reliably describe the dynamical behaviour. This is
the case, for example, in a number of solid state or biological systems, and it
has motivated a line of research aimed at quantifying the amount of
non-Markovian behaviour in a given model. Within this framework, we investigate
the dynamics of a quantum harmonic oscillator linearly coupled to a bosonic
bath. We focus on Gaussian states, which are suitably treated using a
covariance matrix approach. Concentrating on an entanglement based
non-Markovian behaviour quantifier (NMBQ) proposed by Rivas et. al. [1], we
consider the role that near resonant and off-resonant modes play in affecting
the NMBQ. By using a large but finite bath of oscillators for both Ohmic and
super Ohmic spectral densities we find, by systematically increasing the
coupling strength, initially the near resonant modes provide the most
significant non-Markovian effects, while after a certain threshold of coupling
strength the off-resonant modes play the dominant role. We also consider the
NMBQ for two other models where we add a single strongly coupled oscillator to
the model in extra bath mode and 'buffer' configurations, which affects the
modes that determine non-Markovian behaviour.
