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Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays

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  • Wei, Zhouchao
  • Zhu, Bin
  • Yang, Jing
  • Perc, Matjaž
  • Slavinec, Mitja

Abstract

The impact of multiple time delays on the dynamics of two disc dynamos with viscous friction is studied in this paper. We consider the stability of equilibrium states for different delay values, and determine the location of relevant Hopf bifurcations using the normal form method and the center manifold theory. By performing numerical calculations and analysis, we verify the validity of our analytically obtained results. Our research results reveal a classical period-doubling route towards deterministic chaos in the studied system, and play an important role for the better understanding of the complex dynamics of two disc dynamos with viscous friction subject to multiple time delays.

Suggested Citation

  • Wei, Zhouchao & Zhu, Bin & Yang, Jing & Perc, Matjaž & Slavinec, Mitja, 2019. "Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 265-281.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:265-281
    DOI: 10.1016/j.amc.2018.10.090
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    References listed on IDEAS

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    1. Li, Chunbiao & Sprott, Julien Clinton & Kapitaniak, Tomasz & Lu, Tianai, 2018. "Infinite lattice of hyperchaotic strange attractors," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 76-82.
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    3. Fister, Iztok & Perc, Matjaž & Kamal, Salahuddin M. & Fister, Iztok, 2015. "A review of chaos-based firefly algorithms: Perspectives and research challenges," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 155-165.
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    Cited by:

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    2. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    3. Zare, Shahryar & Tavakolpour-Saleh, A.R. & Binazadeh, T., 2023. "Analytical investigation of free piston Stirling engines using practical stability method," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Navid Moghadam, Nastaran & Nazarimehr, Fahimeh & Jafari, Sajad & Sprott, Julien C., 2020. "Studying the performance of critical slowing down indicators in a biological system with a period-doubling route to chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    5. Deng, Shuning & Ji, Jinchen & Wen, Guilin & Xu, Huidong, 2021. "A comparative study of the dynamics of a three-disk dynamo system with and without time delay," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    6. Yang, Bowen & Liu, Ping, 2019. "Global stability and Hopf bifurcation of a three-component model for cell production systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 478-489.

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