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Hysteresis phenomena are common in numerous physical, mechanical,
ecological and biological systems. They reflect memory effects and
process irreversibility. The use of hysteresis operators
(hysterons) offers an approach to macroscopic modelling of the
dynamics of phase transitions and rheological systems. The
applications cover processes in electromagnetism, elastoplasticity
and population dynamics in particular. Hysterons are also typical
elements of control systems where they represent thermostats and
other discontinuous controllers with memory. The book offers the
first systematic mathematical treatment of hysteresis
nonlinearities. Construction procedures are set up for hysterons in
various function spaces, in continuous and discontinuous cases. A
general theory of variable hysterons is developed, including
identification and stability questions. Both deterministic and
non-deterministic hysterons are considered, with applications to
the study of feedback systems. Many of the results presented -
mostly obtained by the authors and their scientific group - have
not been published before. The book is essentially self contained
and is addressed both to researchers and advanced students.
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