  A diffusing lion pursues a diffusing lamb when both of them are allowed to
get back to their homes intermittently. Identifying the system with a pair of
vicious random walkers, we study their dynamics under Poissonian and sharp
resetting. In absence of any resets, the location of intersection of the two
walkers follows a Cauchy distribution. In presence of resetting, the
distribution of the location of annihilation is composed of two parts: one in
which the trajectories cross without being reset (center) and the other where
trajectories are reset at least once before they cross each other (tails). We
find that the tail part decays exponentially for both the resetting protocols.
The central part of the distribution, on the other hand, depends on the nature
of the restart protocol, with Cauchy for Poisson resetting and Gaussian for
sharp resetting. We find good agreement of the analytical results with
numerical calculations.
