  For systems out of equilibrium and subjected to a static bias force it can
often be expected that particle transport will usually follow the direction of
this bias. However, counter-examples exist where particles exhibit uphill
motion (known as absolute negative mobility - ANM), particularly in the case of
coupled particles. Examples in single particle deterministic systems are less
common. Recently, in one such example, uphill motion was shown to occur for an
inertial driven and damped particle in a spatially symmetric periodic
potential. The source of this anomalous transport was a combination of two
periodic driving signals which together are asymmetric under time reversal. In
this paper we investigate the phenomena of ANM for a deterministic particle
evolving in a periodic and symmetric potential subjected to an external
unbiased periodic driving and nonuniform space- dependent damping. It will be
shown that this system exhibits a complicated response behaviour as certain
control parameters are varied, most notably being, enhanced parameter regimes
exhibiting ANM as the static bias force is increased. Moreover, the solutions
exhibiting ANM are shown to be, at least over intermediate time periods,
superdiffusive, in contrast to the solutions that follow the bias where the
diffusion is normal.
