We study a nonlinear response of the underdamped generalized Frenkel-Kontor
ova model (a system of interacting atoms placed into an external periodic p
otential) on the de driving force. Both studied variants of the model, one
with a transverse degree of freedom, and another with two-dimensional isotr
opic substrate potential, exhibit an interesting "fuse"-like behavior: at s
mall forces the system is in the regime of running kinks with a nonzero con
ductivity, while at higher farces the system is trapped in an immobile stat
e. This behavior is explained in terms of a dynamical transition between tw
o states of kinks.