Complex pathways in models of coupled hysterons

Collections of two-state hysteretic elements called hysterons form a popular model to describe the intricate pathways, hysteresis loops and memory effects exhibited by driven complex media. While most studies have focused on independent hysterons, here we show that hysteron interactions have a dramatic effect on the qualitative nature and variety of these pathways and memory effects. Anti-ferromagnetic couplings in particular have a striking impact: hysteresis loops are no longer nested, subharmonic responses can arise, the distinction of ’up’ and ’down’ transitions become blurred, and in some cases the transition graph can only be described as a multi-graph. This work opens up new routes to study pathways and memory in complex media.