Hysteretic benchmark with a dynamic nonlinearity

Hysteresis is a phenomenology commonly encountered in very diverse engineering and science disciplines, ranging from solid mechanics, electromagnetism and aerodynamics [1, 2, 3] to biology, ecology and psychology [4, 5, 6]. The defining property of a hysteretic system is the persistence of an input-output loop as the input frequency approaches zero [7]. Hysteretic systems are inherently nonlinear, as the quasi-static existence of a loop requires an input-output phase shift different from 0 and 180 degrees, which are the only two options offered by linear theory. The root cause of hysteresis is multistability [8]. A hysteretic system possesses multiple stable equilibria, attracting the output depending on the input history. In this sense, it is appropriate to refer hysteresis as system nonlinear memory.