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Z2-symmetric Bogdanov–Takens bifurcation and geomagnetic reversal dynamics in the segmented disc dynamo

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  • Yang, Shuangling

Abstract

The segmented disc dynamo (SDD) is a simplified model for studying the generation and evolution of the Earth’s magnetic field. In this work we show that the SDD model can exhibit a Z2-symmetric Bogdanov–Takens bifurcation of codimension two. This leads us to uncover previously unreported behaviors such as homoclinic and heteroclinic orbits, asymmetric double limit cycles, and triple limit cycles. Importantly, these findings offer a dynamical explanation for the geomagnetic reversal phenomena, demonstrating how the SDD model can transition between distinct steady states corresponding to opposite magnetic field directions via heteroclinic loops. To establish our main result, we develop a systematic approach for analyzing the unfolding of Z2-symmetric Bogdanov–Takens bifurcations of codimension two, which is also suitable for examining similar bifurcations in a broad range of dynamical systems.

Suggested Citation

  • Yang, Shuangling, 2025. "Z2-symmetric Bogdanov–Takens bifurcation and geomagnetic reversal dynamics in the segmented disc dynamo," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012366
    DOI: 10.1016/j.chaos.2025.117223
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    References listed on IDEAS

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    1. Wei, Zhouchao & Akgul, Akif & Kocamaz, Uğur Erkin & Moroz, Irene & Zhang, Wei, 2018. "Control, electronic circuit application and fractional-order analysis of hidden chaotic attractors in the self-exciting homopolar disc dynamo," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 157-168.
    2. Algaba, A. & Fernández-Sánchez, F. & Merino, M. & Rodríguez-Luis, A.J., 2024. "Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Algaba, A. & Fernández-Sánchez, F. & Merino, M. & Rodríguez-Luis, A.J., 2025. "A new kind of T-point in the Lorenz system with a different bifurcation set," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
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