  We consider the damped and driven dynamics of two interacting particles
evolving in a symmetric and spatially periodic potential. The latter is exerted
to a time-periodic modulation of its inclination. Our interest is twofold:
Firstly we deal with the issue of chaotic motion in the higher-dimensional
phase space. To this end a homoclinic Melnikov analysis is utilised assuring
the presence of transverse homoclinic orbits and homoclinic bifurcations for
weak coupling allowing also for the emergence of hyperchaos. In contrast, we
also prove that the time evolution of the two coupled particles attains a
completely synchronised (chaotic) state for strong enough coupling between
them. The resulting `freezing of dimensionality' rules out the occurrence of
hyperchaos. Secondly we address coherent collective particle transport provided
by regular periodic motion. A subharmonic Melnikov analysis is utilised to
investigate persistence of periodic orbits. For directed particle transport
mediated by rotating periodic motion we present exact results regarding the
collective character of the running solutions entailing the emergence of a
current. We show that coordinated energy exchange between the particles takes
place in such a manner that they are enabled to overcome - one particle
followed by the other - consecutive barriers of the periodic potential
resulting in collective directed motion.
