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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 (Odavić  et al  2017  Commun. Nonlinear Sci. Numer. Simul.  47 , 100) 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.

Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force