Representation of hysteresis operators for vector-valued inputs by functions on strings

In 1996, Brokate and Sprekels have shown that scalar-valued hysteresis operators for scalar-valued continuous input functions being piecewise monotone can be uniquely represented by functionals defined on the set of all finite alternating strings of real numbers. In this work, it is shown that a sim...

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Bibliographic Details
Published in:Physica. B, Condensed matter Condensed matter, 2012-05, Vol.407 (9), p.1399-1400
Main Author: Klein, Olaf
Format: Article
Language:English
Subjects:
Condensed matter
Dealing
Exact sciences and technology
Functionals
Hysteresis
Hysteresis operators
Mathematical analysis
Operators
Physics
Representations
Statistical physics, thermodynamics, and nonlinear dynamical systems
Strings
Thermodynamics
Vectorial hysteresis
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Summary:In 1996, Brokate and Sprekels have shown that scalar-valued hysteresis operators for scalar-valued continuous input functions being piecewise monotone can be uniquely represented by functionals defined on the set of all finite alternating strings of real numbers. In this work, it is shown that a similar result can also be derived for hysteresis operators dealing with inputs in a general normed vector space. Considering hysteresis operators defined for continuous inputs that are piecewise monotaffine, it will be shown that these operators can be uniquely represented by functionals acting on an appropriate set of finite strings of elements of this space.
ISSN:0921-4526
1873-2135
DOI:10.1016/j.physb.2011.10.015