Targeting transitions in a system of coupled mechanical hysterons

Many of the complex behaviors exhibited by disordered matter can be captured by modeling the system using elementary units of hysteresis. These units are characterized by a hysteretic relation between two conjugate physical variables, such as pressure and volume, force and displacement, current and voltage etc. In this work, we study mechanical rotors connected to a global driving field and to other rotors through springs, allowing for the creation of both ferromagnetic and antiferromagnetic interactions between the rotors. This offers a large space of geometric parameters that can be varied to realize desired collective behavior. We study the effects of bifurcation points that emerge with varying global driving field on the topology of the configuration space, as well as their effect on the transition graphs of the system. We then investigate methods to find necessary geometric parameters to achieve target transition graphs for a certain number of hysterons.