Nonlinear friction in the periodic stick-slip motion of coupled oscillators

We suggest that coupling-induced orbit hopping is one possible mechanism for stick-slip dynamics. This mechanism is dominant in the highly nonlinear regime. Our example is a one-dimensional array of nonlinearly coupled oscillators subject to a strong periodic potential. The nonlinear dynamics leads to a fundamentally different friction law, in particular when the driving force is barely larger than the minimal force needed to start motion. We find a dramatic increase in the friction coefficient of the array compared to that of a single uncoupled oscillator, even though the same constant force f is applied to each oscillator in the array. The sliding friction coefficient {η} is found to diverge as {η} {∝} ({κ}-κc )^-1/2 , where κc is the critical value of the coupling constant {κ}. The coefficient {η} also grows linearly with the number of elements in the array N and shows dynamical transitions as the external force f applied to each of the oscillators is increased.