Double Periodicity and Frequency-Locking in the Langford Equation

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dc.creatorUmeki, Makoto
dc.date2007-07-05
dc.date.accessioned2026-07-07T08:14:08Z
dc.date.available2026-07-07T08:14:08Z
dc.descriptionThe bifurcation structure of the Langford equation is studied numerically in detail. Periodic, doubly-periodic, and chaotic solutions and the routes to chaos via coexistence of double periodicity and period-doubling bifurcations are found by the Poincaré plot of successive maxima of the first mode $x_1$. Frequency-locked periodic solutions corresponding to the Farey sequence $F_n$ are examined up to $n=14$. Period-doubling bifurcations appears on some of the periodic solutions and the similarity of bifurcation structures between the sine-circle map and the Langford equation is shown. A method to construct the Poincaré section for triple periodicity is proposed.
dc.description9 pages, 10 figures, 2 tables, submitted to JJIAM
dc.identifierhttps://arxiv.org/abs/0707.0769
dc.identifierhttp://arxiv.org/abs/0707.0769
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133017
dc.subjectFluid Dynamics
dc.subjectGeneral Physics
dc.titleDouble Periodicity and Frequency-Locking in the Langford Equation
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