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Biquadratic nontwist map: a model for shearless bifurcations

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  • Grime, Gabriel C.
  • Roberto, Marisa
  • Viana, Ricardo L.
  • Elskens, Yves
  • Caldas, Iberê L.

Abstract

Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection–collision sequences and shearless invariant curves that act as transport barriers in the phase space. Although reported in numerical investigations, the shearless bifurcation, i.e., the emergence scenario of multiple shearless curves, is not well understood. In this work, we derive an area-preserving map as a local approximation of a particle transport model for confined plasmas. Multiple shearless curves are found in this area-preserving map, with the same shearless bifurcation scenario numerically observed in the original model. Due to its symmetry properties and simple functional form, this map is proposed as a model to study shearless bifurcations.

Suggested Citation

  • Grime, Gabriel C. & Roberto, Marisa & Viana, Ricardo L. & Elskens, Yves & Caldas, Iberê L., 2023. "Biquadratic nontwist map: a model for shearless bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001327
    DOI: 10.1016/j.chaos.2023.113231
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    References listed on IDEAS

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    1. Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
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    1. Grime, Gabriel C. & Roberto, Marisa & Viana, Ricardo L. & Elskens, Yves & Caldas, Iberê L., 2023. "Shearless curve breakup in the biquadratic nontwist map," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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