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FFT bifurcation: A tool for spectrum analyzing of dynamical systems

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

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.

Suggested Citation

  • Zandi-Mehran, Nazanin & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Ghosh, Dibakar & Jafari, Sajad & Chen, Guanrong, 2022. "FFT bifurcation: A tool for spectrum analyzing of dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    • Handle: RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000728
    DOI: 10.1016/j.amc.2022.126986
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    References listed on IDEAS

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    1. Zonghua Liu, 2010. "Chaotic Time Series Analysis," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-31, April.
    2. Panahi, Shirin & Nazarimehr, Fahimeh & Jafari, Sajad & Sprott, Julien C. & Perc, Matjaž & Repnik, Robert, 2021. "Optimal synchronization of circulant and non-circulant oscillators," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    3. Gu, Shuangquan & He, Shaobo & Wang, Huihai & Du, Baoxiang, 2021. "Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    Cited by:

    1. Lampartová, Alžběta & Lampart, Marek, 2024. "Exploring diverse trajectory patterns in nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Chafi, Mohammadreza Shafiee & Narm, Hossein Gholizade & Kalat, Ali Akbarzadeh, 2023. "Chaotic and stochastic evaluation in Fluxgate magnetic sensors," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Rajagopal, Karthikeyan & Karthikeyan, Anitha, 2022. "Spiral waves and their characterization through spatioperiod and spatioenergy under distinct excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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