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Using the basin entropy to explore bifurcations

Author

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

Abstract

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear dynamical systems often hide their secrets and the ultimate resource is the numerical simulation of the equations. This paper presents a method to explore bifurcations by using the basin entropy. This measure of the unpredictability can detect transformations of phase space structures as a parameter evolves. We present several examples where the bifurcations in the parameter space have a quantitative effect on the basin entropy. Moreover, some transformations, such as the basin boundary metamorphoses, can be identified with the basin entropy but are not reflected in the bifurcation diagram. The correct interpretation of the basin entropy plotted as a parameter extends the numerical exploration of dynamical systems.

Suggested Citation

  • Wagemakers, Alexandre & Daza, Alvar & Sanjuán, Miguel A.F., 2023. "Using the basin entropy to explore bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008640
    DOI: 10.1016/j.chaos.2023.113963
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    References listed on IDEAS

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    1. Daza, Alvar & Wagemakers, Alexandre & Sanjuán, Miguel A.F., 2022. "Classifying basins of attraction using the basin entropy," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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