  The comb model is a simplified description for anomalous diffusion under
geometric constraints. It represents particles spreading out in a
two-dimensional space where the motions in the x-direction are allowed only
when the y coordinate of the particle is zero. Here, we propose an extension
for the comb model via Langevin-like equations driven by fractional Gaussian
noises (long-range correlated). By carrying out computer simulations, we show
that the correlations in the y-direction affect the diffusive behavior in the
x-direction in a non-trivial fashion, resulting in a quite rich diffusive
scenario characterized by usual, superdiffusive or subdiffusive scaling of
second moment in the x-direction. We further show that the long-range
correlations affect the probability distribution of the particle positions in
the x-direction, making their tails longer when noise in the y-direction is
persistent and shorter for anti-persistent noise. Our model thus combines and
allows the study/analysis of the interplay between different mechanisms of
anomalous diffusion (geometric constraints and long-range correlations) and may
find direct applications for describing diffusion in complex systems such as
living cells.
