  Interaction between extended defects and impurities lies at the heart of many
physical phenomena in materials science. Here we revisit the ubiquitous problem
of the driven motion of an extended defect in a field of mobile impurities,
which self-organize to cause drag on the defect. Under a wide range of external
conditions (e.g. drive), the defect undergoes a transition from slow to fast
motion. This transition is commonly hysteretic: the defect either moves slow or
fast, depending on the initial condition. We explore such hysteresis via a
kinetic Monte Carlo spin simulation combined with computational
coarse-graining. Obtaining bifurcation diagrams (stable and unstable branches),
we map behavior regimes in parameter space. Estimating fast-slow switching
times, we determine whether a simulation or experiment will exhibit hysteresis
depending on observation conditions. We believe our approach is applicable to
quantifying hysteresis in a wide range of physical contexts.
