  We study the asymptotic behavior of trajectories of the continuous dynamical
system (CDS) associated to the the discrete viscosity approximation method for
fixed point problem of nonexpansive mapping (DDS) which was introduced by
Moudafi in 2000 [A. Moudafi, Viscosity approximation methods for fixed points
problems, J. Math. Anal. Appl. 241 (2000), 46-55]. We establish that the
trajectories $x(t)$ of the system (CDS) and the sequences $(x_{n})$ generated
by the the discrete process (DDS) have a very similar asymptotic behaviors.
