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On the dynamics: existence of chaos and symmetry in Krause and Robert (KR) flow

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Abstract

A detailed analytical and numerical investigation of Krause and Robert (KR) flow is done in this article. KR flow is directly derived from magnetohydrodynamics (MHD) equations by using dynamo theory that describes the process through which a rotating, convecting and electrically conducting fluid acts to maintain a magnetic field. The present work focuses on describing complex behavior and symmetry in KR flow. The existence of symmetry has a profound and far-reaching impact on the properties of solution of chaotic dynamical systems. The relation between the KR chaotic attractor with twofold symmetry and its projected image without symmetry is shown in this article. Chaotic behavior of KR flow is studied through Lyapunov spectrum and boundedness to specify the chaotic region. Moreover, the computation of the Hamilton energy shows that KR flow depends on all its variables and, therefore, enough energy is critical to generate wings of KR flow.

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Acknowledgements

We are thankful to Higher Education Commission (HEC), Pakistan, and Institute of Space Technology (IST), Pakistan, for providing a good atmosphere to complete this research work.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan

    Anam Azam & Muhammad Aqeel

  2. Department of Biomedical Engineering, School of Medicine, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Zakir Hussain

  3. Department of Mathematics, COMSATS, University Islamabad, Abbottabad Campus, Islamabad, 22060, Pakistan

    Zakir Hussain

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  1. Anam Azam
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  2. Muhammad Aqeel
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  3. Zakir Hussain
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Correspondence to Anam Azam.

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Communicated by V. Loia.

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Azam, A., Aqeel, M. & Hussain, Z. On the dynamics: existence of chaos and symmetry in Krause and Robert (KR) flow. Soft Comput 25, 2521–2530 (2021). https://doi.org/10.1007/s00500-020-05325-5

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