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Double Periodicity and Frequency-Locking in the Langford Equation by Umeki, Makoto is a scholarly article available to read on EtoBox.

What is Double Periodicity and Frequency-Locking in the Langford Equation about?

The 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 Poincar\'e 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 Poincar\'e section for triple periodicity is proposed.

Author

Umeki, Makoto

Published

2007

Language

EN