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The Shunted Homopolar Dynamo—An Analytic Approach to a PoincarĂ© Map

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We study the set of ordinary differential equations governing the homopolar disk dynamo. It is found that this set, which is a modification of the Lorenz system, has strange attractors of Lorenz type when R (which corresponds to the Rayleigh number of the Lorenz system) tends to infinity. A central aspect of this study is that the Poincare map for this limit can be obtained through Melnikov's perturbation method, in contrast to the usual dependence on numerical computation.
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Document Type: Research Article

Affiliations: Massachusetis Institute of Technology

Publication date: June 1, 1989

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