Double Periodicity and Frequency-Locking in the Langford Equation
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 Poincar\'e plot of successive maxima of the first mode x1. Frequency-locked periodic solutions corresponding to the Farey sequence Fn 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.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.