Bifurcations from steady sliding to stick slip in boundary lubrication

We explore the nature of the transitions between stick slip and steady sliding in models for boundary lubrication introduced in J. M. Carlson and A. A. Batista, Phys. Rev. E 53, 4153 (1996). The models are based on the rate and state approach which has been very successful in characterizing the behavior of dry interfaces [A. Ruina, J. Geophys. Res. 88, 10 359 (1983)]. Our models capture the key distinguishing features associated with surfaces separated by a few molecular layers of lubricant. Here we find that the transition from steady sliding to stick slip is typically discontinuous and sometimes hysteretic. When hysteresis is observed it is associated with a subcritical Hopf bifurcation. In either case, we observe a sudden and discontinuous onset in the amplitude of oscillations at the bifurcation point.