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Classifying basins of attraction using the basin entropy

Author

Listed:
  • Daza, Alvar
  • Wagemakers, Alexandre
  • Sanjuán, Miguel A.F.

Abstract

A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections between the basin entropy and other measures used to characterize the unpredictability associated to the basins of attraction, such as the uncertainty exponent, the lacunarity or other different parameters related to the Wada property.

Suggested Citation

  • Daza, Alvar & Wagemakers, Alexandre & Sanjuán, Miguel A.F., 2022. "Classifying basins of attraction using the basin entropy," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003228
    DOI: 10.1016/j.chaos.2022.112112
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    References listed on IDEAS

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    1. Gusso, André & de Mello, Leandro E., 2021. "Fractal dimension of basin boundaries calculated using the basin entropy," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
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    Cited by:

    1. Ostrovskii, Valerii Yu. & Rybin, Vyacheslav G. & Karimov, Artur I. & Butusov, Denis N., 2022. "Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Wagemakers, Alexandre & Daza, Alvar & Sanjuán, Miguel A.F., 2023. "Using the basin entropy to explore bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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