The authors investigate some continuous and discrete dynamics for solving inclusions of the form \[ \partial\Phi (x) + B(x)\ni 0, \] where \(\partial\Phi\) is the subdifferential of a convex lower semicontinuous function \(\Phi: H \rightarrow \mathbb{R}\cup \{ +\infty \}\), \(H\) is a Hilbert space and \(B: H\rightarrow H\) is a monotone cocoercive operator. Their analysis is based on the convergence properties of the orbits of the continuous dynamical systems \[ v(t)\in \partial\Phi (x(t)), \] and \[ \lambda x'(t)+v'(t)+v(t)+ B(x(t))=0,\;\lambda>0. \] By a discretization of the time \(t\) of the above systems, the authors give some convergence properties of the backward-forward (BF) algorithm. Some convergence properties of the orbits of the semigroup generated by \(-(\partial\Phi+B)\) are investigated. Finally, a link with the classical (FB) algorithm is given.