Stability properties of periodically driven overdamped pendula and their implications to physics of semiconductor superlattices and Josephson junctions
| Autor: | Kirill N. Alekseev, Jukka Isohätälä |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Josephson effect
Physics Condensed Matter - Mesoscale and Nanoscale Physics Applied Mathematics Degenerate energy levels Pendulum FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Mathematical Physics (math-ph) Pattern Formation and Solitons (nlin.PS) Nonlinear Sciences - Pattern Formation and Solitons Nonlinear system Pitchfork bifurcation Classical mechanics Linear differential equation Ordinary differential equation Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Mathematical Physics Bifurcation |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science. 20:023116 |
| ISSN: | 1089-7682 1054-1500 |
| DOI: | 10.1063/1.3382087 |
| Popis: | We consider the first order differential equation with a sinusoidal nonlinearity and periodic time dependence, that is, the periodically driven overdamped pendulum. The problem is studied in the case that the explicit time-dependence has symmetries common to pure ac-driven systems. The only bifurcation that exists in the system is a degenerate pitchfork bifurcation, which describes an exchange of stability between two symmetric nonlinear modes. Using a type of Prufer transform to a pair of linear differential equations, we derive an approximate condition of the bifurcation. This approximation is in very good agreement with our numerical data. In particular, it works well in the limit of large drive amplitudes and low external frequencies. We demonstrate the usefulness of the theory applying it to the models of pure ac-driven semiconductor superlattices and Josephson junctions. We show how the knowledge of bifurcations in the overdamped pendulum model can be utilized to describe effects of rectification and amplification of electric fields in these microstructures. Comment: 15 pages, 7 figures, Revtex 4.1. Revised and expanded following referee's report. Submitted to journal Chaos. |
| Databáze: | OpenAIRE |
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