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FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions

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  • L. Borkowski
  • A. Stefanski

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.

Suggested Citation

  • L. Borkowski & A. Stefanski, 2015. "FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, December.
  • Handle: RePEc:hin:jnlmpe:367036
    DOI: 10.1155/2015/367036
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    Cited by:

    1. Molaie, Moslem & Samani, Farhad S. & Zippo, Antonio & Iarriccio, Giovanni & Pellicano, Francesco, 2023. "Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Barba-Franco, J.J. & Gallegos, A. & Jaimes-ReƔtegui, R. & Pisarchik, A.N., 2022. "Dynamics of a ring of three fractional-order Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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