Dept. of Appl.Math @ ucc.ie

Systems with Hysteresis
Welcome

Contents

What is `Hysteresis'

Preisach Model

Closed loop systems

Complex behavior

Other Hysterons

Advanced modelling

Bibliography

Bibliography

1
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2
Brokate M. and Pokrovskii A.V., Asymptotically stable periodic oscillation in systems with hysteresis nonlinearities, J. Diff. Eq., 150 (1998), 98-123.

3
Brokate M. and Sprekels J., ``Hysteresis and Phase Transitions'', Springer-Verlag, Berlin, 1996.

4
Cross R. and Allan A., On the history of hysteresis. In Unemployment, Hysteresis & Natural Rate Hypothesis, Rod Cross ed., Blackwell, 1988, pp. 26-38.

5
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6
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7
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8
Gilman T.S. and Pokrovskii A.V., Forced vibrations of an oscillator with hysteresis taken into account, Soviet Mathematics Doklady, 25 (1982), No 2, pp. 424 - 427.

9
Kluwer Encyclopedia of Mathematics, Supplement Volume 1, 1997, Kluwer Acad. Publ. pp. 310,384.

10
Krasnosel'skii M. and Pokrovskii A., ``Systems with Hysteresis'', Springer-Verlag, New York, 1989.

11
Krejci P., ``Hysteresis, Convexity and Dissipation in Hyperbolic Equations'', Gakkotosho, Tokio, 1996.

12
Krejci P. and Sprekels J., in Variations of domain and free-boundary problems in solid mechanics (Paris, 1997), 237-244, Kluwer Acad. Publ., Dordrecht, 1999.

13
Mayergoyz I.D. Mathematical Models of Hysteresis, Springer-Verlag, 1991.

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O'Malley, R. E., Jr., Naive singular perturbation theory. Special issue in memory of Richard Weiss. Math. Models Methods Appl. Sci. 11 (2001), no. 1, 119-131.

15
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16
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17
Pokrovskii A., Shuttle algorithm in analysis of systems with hysteresis nonlinearities, In: ``Models of Hysteresis'', (A. Visintin, ed.), Pitman Research Notes in Mathematics Series, 286, Longman Sci. Tech., Harlow, 1993, pp. 124 - 142.

18
Pokrovskii A., Topological shadowing and split-hyperbolicity, Journal for Difference and Differential Equations, special issue dedicated to M.A. Krasnosel'skii. Funct. Differ. Equ. 4 (1997), no. 3-4, 335-360 (1998).

19
Preisach P., Über die magnetische Nachwirkung. Zeitschrift für Physik, 94 (1938), 277-302.

20
Rasskazov O., Forward and Backward Stable Sets of Split-hyperbolic Mappings. Russian Academy of Natural Sciences. Transactions. Mathematics, Mathematical Modeling, Informatics & Control, 5 (2001), No 1-2, pp. 185-205.

21
Rauch L.L. Ann. Maths. Studies, 20 (1950).

22
Visintin A., ``Differential Models of Hysteresis'', Berlin, Springer, 1994.