Invariant submanifold for series arrays of Josephson junctions
| Autor: | Steven H. Strogatz, Seth A. Marvel |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Josephson effect
Invariant manifold General Physics and Astronomy FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas Linearization Oscillometry 0103 physical sciences Poisson Distribution Invariant (mathematics) 010306 general physics Mathematical Physics Ansatz Physics Models Statistical Applied Mathematics Mathematical analysis Statistical and Nonlinear Physics Equipment Design Models Theoretical Submanifold Nonlinear Sciences - Adaptation and Self-Organizing Systems Nonlinear Dynamics Phase space Adaptation and Self-Organizing Systems (nlin.AO) Algorithms Curse of dimensionality |
| DOI: | 10.48550/arxiv.0812.4481 |
| Popis: | We study the nonlinear dynamics of series arrays of Josephson junctions in the large-N limit, where N is the number of junctions in the array. The junctions are assumed to be identical, overdamped, driven by a constant bias current and globally coupled through a common load. Previous simulations of such arrays revealed that their dynamics are remarkably simple, hinting at the presence of some hidden symmetry or other structure. These observations were later explained by the discovery of (N - 3) constants of motion, each choice of which confines the resulting flow in phase space to a low-dimensional invariant manifold. Here we show that the dimensionality can be reduced further by restricting attention to a special family of states recently identified by Ott and Antonsen. In geometric terms, the Ott-Antonsen ansatz corresponds to an invariant submanifold of dimension one less than that found earlier. We derive and analyze the flow on this submanifold for two special cases: an array with purely resistive loading and another with resistive-inductive-capacitive loading. Our results recover (and in some instances improve) earlier findings based on linearization arguments. Comment: 10 pages, 6 figures |
| Databáze: | OpenAIRE |
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