FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions

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 ty...

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Bibliographic Details
Published in:Mathematical problems in engineering 2015-01, Vol.2015 (2015), p.1-9
Main Authors: Borkowski, L., Stefanski, A.
Format: Article
Language:English
Subjects:
Bifurcations
Chaos theory
Complement
Duffing oscillators
Dynamic tests
Dynamical systems
Fourier transforms
Frequency analysis
Frequency distribution
Liapunov exponents
Lyapunov exponents
Mathematical analysis
Nonlinear dynamics
Oscillators
Parameter identification
Studies
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2015/367036