  In this paper, we approach the problem of finding the zeros of the sum of a
maximally monotone operator and a monotone and Lipschitz continuous one in a
real Hilbert space via an implicit forward-backward-forward dynamical system
with nonconstant relaxation parameters and stepsizes of the resolvents. Besides
proving existence and uniqueness of strong global solutions for the
differential equation under consideration, we show weak convergence of the
generated trajectories and, under strong monotonicity assumptions, strong
convergence with exponential rate. In the particular setting of minimizing the
sum of a proper, convex and lower semicontinuous function with a smooth convex
one, we provide a rate for the convergence of the objective function along the
ergodic trajectory to its minimum value.
