  We investigate the coherence and non-Markovianity of a quantum tunneling
system whose barrier is fluctuated by a telegraph noise, and its energy gap is
modulated by Gaussian noise. With the help of averaging method, the system
dynamics are analytically derived, and the analytical expression for coherence
measure and non-Markovianity for the very limited parameter regimes for both
initially coherent and non-coherent states are obtained. We observe
non-Markovian dynamics in a situation where the Kubo number is high. It is also
found that there is no strong relation between the coherence of the system and
non-Markovianity dynamics except in a region in which these two tend to change
their behavior at the intermediate noise color for two initial states.
