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

Shuangling Yang

Chaos, Solitons & Fractals, 2025, vol. 201, issue P2

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.

Keywords: Segmented disc dynamo; Homoclinic orbits; Heteroclinic orbits; Bogdanov–Takens bifurcation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012366

DOI: 10.1016/j.chaos.2025.117223

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