Hysteresis behavior patterns in complex systems

Many complex systems such as magnets, shape memory alloys, as well as socioeconomic and biological systems are known to display hysteresis. This inherently irreversible process differs from the other irreversible processes most often addressed in literature by the memory that persists long after the external parameters stop changing. In general, hysteresis is a consequence of multi-scale system dynamics and the existence of many metastable states. Although hysteresis is typically illustrated by closed minor loops, other types of hysteretic trajectories are often observed where closed loops form gradually after several external parameter periods or not at all. The question arises: What in the structure of a system determines these qualitatively different behaviors of hysteretic trajectories?This thesis models complex hysteretic systems using a network of bistable binary elements and investigates network structure induced changes in hysteretic behavior. The main focus is on studying the minor loop formation processes for a single cyclically varying external parameter. Stable minor loops are observed to form at different rates as a function of the number of cycles, depending on the sign of the interactions, disorder level, and on the connectivity and topology of the interaction networks. For certain dense interaction networks, hysteretic trajectories that do not converge to a minor loop after an arbitrarily large number of external parameter periods are discovered. It is shown that their appearance is related to the presence of specific topological structures in the network. Thus, the thesis demonstrates several interesting links between hysteretic behavior and the underlying structure of complex systems.