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Mathematical Problems in Engineering
Volume 2015, Article ID 367036, 9 pages
Research Article

FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions

Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland

Received 5 August 2015; Revised 25 October 2015; Accepted 1 December 2015

Academic Editor: Jonathan N. Blakely

Copyright © 2015 L. Borkowski and A. Stefanski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.