  The diffusion in the comb structures is a popular model of geometrically
induced anomalous diffusion. In the present work we concentrate on the
diffusion along the backbone in a system where sidebranches are planes, and the
diffusion thereon is anomalous and described by continuous time random walks
(CTRW). We show that the mean squared displacement (MSD) in the backbone of the
comb behaves differently depending on whether the waiting time periods in the
sidebranches are reset after the step in the backbone is done (a rejuvenating
junction model), or not (a non-rejuvenating junction model). In the
rejuvenating case the subdiffusion in the sidebranches only changes the
prefactor in the ultra-slow (logarithmic) diffusion along the backbone, while
in the non-rejuvenating case the ultraslow, logarithmic subdiffusion is changed
to a much faster power-law subdiffusion (with a logarithmic correction) as it
was found earlier by Iomin and Mendez [Chaos Solitons and Fractals 2016;
82:142]. Moreover, in the first case the result does not change if the
diffusion in the backbone is itself anomalous, while in the second case it
does. Two of the special cases of the considered models (the non-rejuvenating
junction under normal diffusion in the backbone, and rejuvenating junction for
the same waiting time distribution in the sidebranches and in junction points)
were also investigated within the approach based on the corresponding
generalized Fokker-Planck equations.
