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Differential equations with hysteresis via a canonical example. (English) Zbl 1142.34026
Bertotti, Giorgio (ed.) et al., The science of hysteresis. Vol. I. Mathematical modeling and applications. Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-369431-7/hbk; 978-0-12-480874-4/set). 125-291 (2006).
A qualitative theory of ordinary differential equations and systems with a scalar hysteresis operator on the right hand side is developed here. Emphasis is put on problems of stability of solutions, boundedness and asymptotic stability, oscillatory behavior, periodicity, and chaos. The theory is illustrated by nice and thoroughly selected numerical examples.
For the entire collection see [Zbl 1117.34045].

MSC:
34C55 Hysteresis for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C12 Monotone systems involving ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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