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Chaos break and synchrony enrichment within Hindmarsh–Rose-type memristive neural models

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Abstract

The fluctuation of ions concentration across the cell membrane of neuron can generate a time varying electromagnetic field. Thus, memristors are used to realize the coupling between the magnetic flux and the membrane potential across the membrane. Such coupling results from the phenomenon of electromagnetic induction in neurons. In this work, we numerically show that the electromagnetic induction phenomenon can firstly suppress chaotic states in a neural setups and secondly enrich neural synchrony in a system of two coupled neurons. By means of the bifurcation diagrams on maximum Lyapunov exponent and interspike interval, we show that increasing in memristor strength delocalizes first, then fully suppresses chaotic states in a single neuron. In a system of two electrically coupled Hindmarsh–Rose-type neurons, we realize that increasing in memristor strength gradually reduces the threshold value of electrical synaptic coupling strength above which a transition to synchronized states is achieved. The transition to synchronized states are determined either by the sign of the maximum transverse Lyapunov exponent or by the magnitude of the synchronization factor. Our results suggest that chaos break in a neurons group by electromagnetic induction phenomenon might automatically release neural synchrony which is involved in information processing and many seizures in the brain.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The corresponding author (A.S. Etémé) is very grateful to all experts who have significantly contributed to the improvement of this paper.

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Authors and Affiliations

  1. Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

    Armand Sylvin Etémé & Henry Paul Ekobena Fouda

  2. Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana

    Conrad Bertand Tabi

  3. National Radiation Protection Agency of Cameroon, P.O. Box 33732, Yaoundé, Cameroon

    Jean Félix Beyala Ateba

  4. Department of Physics, Faculty of Science, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Alidou Mohamadou

  5. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

    Timoléon Crépin Kofané

Authors
  1. Armand Sylvin Etémé
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  2. Conrad Bertand Tabi
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  3. Jean Félix Beyala Ateba
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  6. Timoléon Crépin Kofané
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Correspondence to Armand Sylvin Etémé.

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Etémé, A.S., Tabi, C.B., Beyala Ateba, J.F. et al. Chaos break and synchrony enrichment within Hindmarsh–Rose-type memristive neural models. Nonlinear Dyn 105, 785–795 (2021). https://doi.org/10.1007/s11071-021-06640-8

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  • DOI: https://doi.org/10.1007/s11071-021-06640-8

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