  We study the existence and uniqueness of (locally) absolutely continuous
trajectories of a dynamical system governed by a nonexpansive operator. The
weak convergence of the orbits to a fixed point of the operator is investigated
by relying on Lyapunov analysis. We show also an order of convergence of
$o(\frac{1}{\sqrt{t}})$ for the fixed point residual of the trajectory of the
dynamical system. We apply the results to dynamical systems associated with the
problem of finding the zeros of the sum of a maximally monotone operator and a
cocoercive one. Several dynamical systems from the literature turn out to be
particular instances of this general approach.
