  The survival chance of a prey chased by a predator depends not only on their
relative speeds but importantly also on the local environment they have to
face. For example, a wolf chasing a deer might take a long time to cross a
river which can quickly be crossed by the deer. Here, we propose a simple
predator-prey model for a situation in which both the escaping prey and the
chasing predator have to surmount an energetic barrier. Different
barrier-assisted states of catching or final escaping are classified and
suitable scaling laws separating these two states are derived. We discuss the
effect of fluctuations on the catching times and determine states in which
catching or escaping is more likely. We further identify trapping or escaping
states which are determined by hydrodynamics and chemotactic interactions. Our
results are of importance for both microbes and self-propelled unanimate
microparticles following each other by non-reciprocal interactions in
inhomogeneous landscapes.
