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Elimination of spiral waves in excitable media by magnetic induction

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Abstract

The formation of spiral waves in excitable media is a fascinating example of the beauty of nonlinear dynamics in spatiotemporal systems. Apart from the beauty of the patterns, the subject also has many practical application. For example, the emergence of spiral waves in cardiac tissue can lead to arrhythmias. Cortical spiral waves are also involved in epileptic seizures. Motivated by this, we here study the effects of magnetic induction on the formation of spiral waves in excitable media. An external sinusoidal magnetic induction with different amplitudes and angular frequencies is applied in order to study whether spiral waves could be eliminated. We use a network of coupled neurons as a model for the excitable medium. The four-variable magnetic Hindmarsh–Rose model is used for the local dynamics of each isolated neuron. The distribution of the cell membrane potential over time, affected by magnetic induction, is determined and the results are depicted as snapshots of the 2D network. Our research reveals that the continuance of rotating spiral seeds is impaired by high-amplitude magnetic induction. Moreover, we show that low-frequency induction is not capable of breaking the reorganizing rhythm of the spiral seeds, while much higher frequencies can be too fast to overcome this special rhythm.

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Acknowledgements

Sajad Jafari was supported by the Iran National Science Foundation (Grant No. 96000815). Matjaž Perc was supported by the Slovenian Research Agency (Grants Nos. J1-7009 and P5-0027).

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Authors and Affiliations

  1. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875-4413, Iran

    Zahra Rostami & Sajad Jafari

  2. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia

    Matjaž Perc & Mitja Slavinec

  3. CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, 2000, Maribor, Slovenia

    Matjaž Perc

  4. Complexity Science Hub, Josefstädterstraße 39, 1080, Vienna, Austria

    Matjaž Perc

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  1. Zahra Rostami
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  2. Sajad Jafari
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Correspondence to Matjaž Perc.

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Rostami, Z., Jafari, S., Perc, M. et al. Elimination of spiral waves in excitable media by magnetic induction. Nonlinear Dyn 94, 679–692 (2018). https://doi.org/10.1007/s11071-018-4385-9

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  • DOI: https://doi.org/10.1007/s11071-018-4385-9

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