Abstract
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.
Highlights
The spectral analysis of a signal using the fast Fourier transform (FFT) is a widespread method for investigation and diagnostics of dynamical systems in science and engineering
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
In this paper the dynamical system composed of the ring of seven unidirectionally coupled nonlinear Duffing oscillators is examined using the FFT bifurcation analysis
Summary
The spectral analysis of a signal using the fast Fourier transform (FFT) is a widespread method for investigation and diagnostics of dynamical systems in science and engineering. In many areas of science and technology, we can observe the use of the fast Fourier transform in order to present the results of research and calculations. The use of the FFT analysis to study nonlinear dynamical systems is present in works of many scientists and researchers. Numerical investigations were confirmed by experimental research They used the FFT analysis as a tool for the presentation of results. The FFT analysis is applied to study dynamics and bifurcations of the ring of unidirectionally coupled nonlinear Duffing oscillators. In this system a route to chaos via 2-frequency and 3-frequency quasiperiodicity can be observed.
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