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Stability properties of periodically driven overdamped pendula and their physical implications | | Jukka Isohätälä
; Kirill N. Alekseev
; | | Date: |
6 Nov 2009 | | Abstract: | 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 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 ac-driven semiconductor superlattices and Josephson junctions. | | Source: | arXiv, 0911.1215 | | Services: | Forum | Review | PDF | Favorites | |
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