What is Hysteresis?

Hysteresis is a widely occuring phenomenon. It can be found in a wide variety of natural and constructed systems. Generally, a system is said to exhibit hysteresis when a characteristic looping behaviour of the input-output graph is displayed. These loops can be due to a variety of causes. Furthermore, the input-output graphs of periodic inputs at different frequencies are generally identical. Existing definitions of hysteresis are useful in different contexts but fail to fully characterize it. In this paper, a number of different situations exhibiting hysteresis are described and analyzed. The applications described are: an electronic comparator, gene regulatory network, backlash, beam in a magnetic field, a class of smart materials and inelastic springs. The common features of these widely varying situations are identified and summarized in a final section that includes a new definition for hysteresis.