Array-enhanced friction in the periodic stick-slip motion of nonlinear oscillators

We study the nonlinear contribution to stick-slip motion in a weakly coupled discrete one-dimensional array of oscillators subject to a periodic potential. 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 is found to diverge as $\eta \propto {(\kappa -{\kappa }_c)}^{-\frac{1}{2}}$, where ${\kappa }_c$ is the critical value of the coupling constant $\kappa$, and shows two dynamical transitions as we increase the external force $f$ applied to each of the oscillators.