Article | REF: D92 V1

Ferroresonance in networks - Modeling and applications to circuit typology

Authors: Michel RIOUAL, Jean-Christophe KIENY, Jean MAHSEREDJIAN

Publication date: August 10, 2009

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1. Modeling, adapted mathematical framework

Typical ferroresonance equations can be found in many physical phenomena, such as meteorology (Edward Lorentz in 1963), Rayleigh-Benard thermal convection and the stability of the solar system (Jacques Laskar). Their resolution has aroused the curiosity of many mathematicians [39][40][41] .

Poincaré laid the foundations for this in 1905, when he studied non-integrable systems, such as several bodies in gravitational interaction, for which no time solution of the form f (t ) can be found; note in passing that the description on a plane of the evolution of non-linear systems is called a "Poincaré cut" (cf. §...

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Modeling, adapted mathematical framework