FFT bifurcation : A tool for spectrum analyzing of dynamical systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Nazanin Zandi-Mehran
  • Fahimeh Nazarimehr
  • Karthikeyan Rajagopal
  • Dibakar Ghosh
  • Sajad Jafari

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number126986
Journal / PublicationApplied Mathematics and Computation
Volume422
Online published6 Feb 2022
Publication statusPublished - 1 Jun 2022

Abstract

This paper presents FFT bifurcation as a tool for investigating complex dynamics. Firstly, two well-known chaotic systems (Rössler and Lorenz) are discussed from the frequency viewpoint. Then, both discrete-time and continuous-time systems are studied. Various systems with different properties are discussed. In discrete-time systems, Logistic map and a biological map are investigated. For continuous-time systems, a system with a stable equilibrium, forced van der Pol system, and a system with a line of equilibria are discussed. For each system under investigation, the proposed FFT bifurcation diagrams are compared with the conventional bifurcation diagrams, showing some interesting information uncovered by the FFT bifurcation. For periodic trajectories, the FFT bifurcations show high power at the dominant frequency and harmonics. By doubling the periods, their dominant frequencies are halved, and more harmonics emerge in the studied frequency intervals. For the chaotic dynamics, the FFT bifurcation shows a wideband power spectrum. The FFT bifurcation shows interesting results in comparison to conventional bifurcation diagrams.

Research Area(s)

  • Bifurcation diagram, Dynamical system, FFT bifurcation, Frequency spectrum, Hidden dynamics

Citation Format(s)

FFT bifurcation : A tool for spectrum analyzing of dynamical systems. / Zandi-Mehran, Nazanin; Nazarimehr, Fahimeh; Rajagopal, Karthikeyan; Ghosh, Dibakar; Jafari, Sajad; Chen, Guanrong.

In: Applied Mathematics and Computation, Vol. 422, 126986, 01.06.2022.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review