On the convergence of the trajectories of the dynamical Moudafi’s viscosity approximation system

We study the asymptotic behavior of trajectories of the continuous dynamical system(CDS) associated with the discrete viscosity approximation method for fixed point problem of nonexpansive mapping (DDS) which was introduced by Moudafi (J Math Anal Appl 241:46–55, 2000). We establish that the trajectories x(t) of the continuous dynamical system (CDS) has an asymptotic behavior similar to the behavior of the sequences \((x_{n})\) $(x_n)$ generated by the discrete viscosity approximation (DDS)