  Usually, overdamped Josephson junctions do not exhibit chaotic behaviour in
their phase dynamics, either because the phase space dimension is less than
three (as in the case of a single overdamped ac-driven junction) or due to the
general tendency of systems to become less chaotic with increasing dissipation
(as in the case of coupled overdamped junctions). Here we consider the
so-called $\varphi_0$ S/F/S Josephson junction in which the current flowing
through the junction may induce magnetization dynamics in the ferromagnetic
interlayer, between the two superconducting layers. We find that, due to the
induced magnetization dynamics, even in the overdamped limit, i.e. for a
junction without capacitance, the junction may exhibit chaos and hysteresis
that in some cases leads to multiple branches in its current-voltage
characteristics. We also show that pulsed current signals can result in
switching between different voltage states, a result which is potentially
useful for superconducting memory applications.
