Dept. of Appl.Math @

Systems with Hysteresis


What is `Hysteresis'
   I/O diagrams
   Krasnosel'skii concept

Preisach Model

Closed loop systems

Complex behavior

Other Hysterons

Advanced modelling


What is `Hysteresis'

Hysteresis is a strongly nonlinear phenomenon which occur in many industrial, physical and economic systems. The wording `strongly nonlinear' means that linearisation does not encapsulate the observed phenomena.

The word hysteresis is of the Greek origin and means etymologically `coming behind'. It was introduced into scientific vocabulary about 120 years ago by the Scottish physicist, Alfred Ewing, as follows. ``When there are two quantities $M$ and $N$, such that cyclic variations of $N$ cause cyclic variation of $M$, then if the changes of $M$ lag behind those of $N$, we may say that there is hysteresis in the relation of $M$ and $N$'' [7]. Further interesting historical details are presented in [4].

Nowadays "hysteresis" is one of the most `multi-meaning' terms (like, for example, `entropy'). For example, it is widely used in mechanics (plastic hysteresis) [12], physics (ferromagnetic hysteresis) [13] phase transitions [3], hydrology (soil-moisture hysteresis) [15], and economics (shock analysis) [5].