Dept. of Appl.Math @

Systems with Hysteresis


What is `Hysteresis'

Preisach Model

Closed loop systems

Complex behavior

Other Hysterons

Advanced modelling




The mathematical theory of systems with hysteresis is an exiting new chapter of nonlinear analysis. While based on physical ideas, it also extends them to abstract science, enabling the analysis to be of quite general character. It includes interesting new mathematics and has a wide range of applications in science, engineering and economics.

A key innovation is the work, from the early 1970s, of a group of Russian mathematicians. This group, which was led by Mark Krasnosel'skii, one of the founders of nonlinear analysis, initiated the investigations of hysteresis phenomena using the theory of nonlinear operators. It was my good fortune to become a member of the Krasnosel'skii group at the very beginning.

This home page provides, for beginners, a guided interactive tour to the `courts of Hysteresis'. The topics are chosen to be simple and interesting (in my personal taste).

This homepage was created mainly by two young mathematicians: a PostDoc researcher, Dr. Oleg Rasskazov, and a Masters student, Mark Donegan. This project was supported by Boole Centre for Research in Informatics, by Enterprise Ireland, Grant SC/2000/138 and Grant SC/2003/376 and by IRCSET Embark Ireland Postdoctoral fellowship PD/2004/26.

Prof. Alexei Pokrovskii,
Head of Dept. of Applied Mathematics,
University College, Cork,

P.S. This page is best viewed with Sun's Java Runtime Environment, JRE, that can be downloaded from the official website here.