  Josephson junctions with weak-links of exotic materials allow the elucidation
of the Josephson effect in previously unexplored regimes. Further, such devices
offer a direct probe of novel material properties, for example in the search
for Majorana fermions. In this work, we report on DC and AC Josephson effect of
high-mobility, hexagonal boron nitride (h-BN) encapsulated graphene Josephson
junctions. On the application of RF radiation, we measure phase-locked Shapiro
steps. An unexpected bistability between $\pm 1$ steps is observed with
switching times on the order of seconds. A critical scaling of a bistable state
is measured directly from the switching time, allowing for direct comparison to
numerical simulations. We show such intermittent chaotic behavior is a
consequence of the nonlinear dynamics of the junction and has a sensitive
dependence on the current-phase relation. This work draws connections between
nonlinear phenomena in dynamical systems and their implications for ongoing
condensed matter experiments exploring topology and exotic physics.
