English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the first order differential equation with a sinusoidalnonlinearity and periodic time dependence, that is, the periodically drivenoverdamped pendulum. The problem is studied in the case that the explicittime-dependence has symmetries common to pure ac-driven systems. The onlybifurcation 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, wederive an approximate condition of the bifurcation. This approximation is invery good agreement with our numerical data. In particular, it works well inthe limit of large drive amplitudes and low external frequencies. Wedemonstrate the usefulness of the theory applying it to the models of pureac-driven semiconductor superlattices and Josephson junctions. We show how theknowledge of bifurcations in the overdamped pendulum model can be utilized todescribe effects of rectification and amplification of electric fields in thesemicrostructures.

chaos

Stability properties of periodically driven overdamped pendula and their  implications to physics of semiconductor superlattices and Josephson  junctions