Synchronized stress oscillations in depinning models with aging.

We propose a model that extends the standard depinning paradigm by incorporating an aging mechanism into the local pinning force. This favors oscillations between a stuck state of large pinning and a slipping state of smaller pinning. We show that for mean field interactions between sites this mechanism can lead to the appearance of "king avalanches" and global instabilities, producing a global oscillatory stick-slip stress regime. We construct the phase diagram for this mean field case and identify regions of smooth dynamics, pure stick-slip, and bistability. Crucially, when considering two-dimensional systems with short-range interactions we find that states of global stress oscillation persist, but in contrast to the mean field case, no system-size avalanches appear. Instead, we observe alternating temporal intervals of larger and lower avalanche activity that correlate with the stress oscillations.