Double Periodicity and Frequency-Locking in the Langford Equation
arXiv:0707.0769
Abstract
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 Poincaré plot of successive maxima of the first mode . Frequency-locked periodic solutions corresponding to the Farey sequence are examined up to . 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.
9 pages, 10 figures, 2 tables, submitted to JJIAM