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New insights into the extended Malkus-Robbins dynamo

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  • Chen, Xitong
  • Bao, Jianghong
  • Yu, Huanyu

Abstract

The present work is devoted to giving new insights into the extended Malkus-Robbins (EMR) dynamo. Firstly, based on differential geometry method, i.e. Kosambi-Cartan-Chern (KCC) theory, the paper investigates the Jacobi stability of the equilibrium and periodic orbit by the eigenvalues of the deviation curvature tensor. The deviation vector is applied to analyze the trajectory behaviors near the equilibrium and periodic orbit. Secondly, the zero-zero-Hopf bifurcation is investigated. The paper obtains the conditions that two periodic solutions appear at the bifurcation point and discusses their stability. Finally, on the global dynamics, the ultimate bound sets of the system are estimated. Numerical simulations are given to verify and visualize the corresponding theoretical results.

Suggested Citation

  • Chen, Xitong & Bao, Jianghong & Yu, Huanyu, 2021. "New insights into the extended Malkus-Robbins dynamo," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003209
    DOI: 10.1016/j.chaos.2021.110966
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    References listed on IDEAS

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    1. Llibre, Jaume & Makhlouf, Amar, 2016. "Zero-Hopf bifurcation in the generalized Michelson system," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 228-231.
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