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Unstable periodic orbits in a Faraday disk dynamo
Author(s) -
Moroz Irene M.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700681
Subject(s) - dynamo , attractor , physics , chaotic , bifurcation , lorenz system , homopolar motor , crisis , periodic orbits , faraday cage , nonlinear system , classical mechanics , mathematical analysis , topology (electrical circuits) , mathematics , computer science , magnetic field , quantum mechanics , artificial intelligence , magnet , combinatorics
Hide et al [2] introduced a system of three nonlinear coupled ordinary differential equations to model a self‐exciting Faraday disk homopolar dynamo. Two examples of chaotic behaviour were shown by them. Moroz [4] performed a more extensive analysis of this dynamo model, including bifurcation transition diagrams and unstable periodic orbits for the two chaotic examples. We now use these unstable periodic orbits to identify a possible template for the chaotic attractor, using ideas from topology [1] and results from a corresponding analysis of the Lorenz attractor. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)