Subharmonic driving response from frustrated interactions and scrambling in a mechanical hysteron system

Disordered systems generally display bumpy energy landscapes, that lead to complex pathways under driving. For some such systems, subharmonic responses have been observed, where it takes multiple driving cycles for the system to return to its initial state. Modelling a disordered system as a collection of interacting hysterons, we attempt to uncover the principles underlying a subharmonic response. Our theoretical model points towards two necessary requirements: first, the hysteron switching order must depend on their collective state (i.e., 'scrambling'), and second, hysteron interactions must be frustrated. We test our findings via an experimental 'snapgami' model for mechanical hysterons.