  The response function and largest Lyapunov exponent analysis were applied to
the driven overdamped Frenkel-Kontorova model with two types of anharmonic
convex interparticle potentials. In both cases model reduces to a single
particle model for integer values of winding number. It is shown that the
mirror image of the amplitude dependence of critical depinning force and
largest Lyapunov exponent observed recently in the standard Frenkel-Kontorova
model [Commun. Nonlinear Sci. Numer. Simul. 47, 100 (2017)] is not retained
generally. Behaviour of systems with relatively strong interparticle force was
examined and evidence for the appearance of mode-locking phenomenon in both
directions of particles' motion is presented.
