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Coexistence of Attractors and Its Control with Selection of a Desired Attractor in a Model of Extended Hindmarsh–Rose Neuron with Nonlinear Smooth Fitting Function: Microcontroller Implementation

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Abstract

Purpose

In this paper, we present a fitted model of the extended Hindmarsh–Rose (eHR) neuron constructed using the hyperbolic tangent composite functions to replace the non-linear polynomial functions present in the original model of the eHR neuron.

Methods

Thus, through classical techniques of analysis of nonlinear systems, we observe complex phenomena generated by this system when the excitation current varies. In addition, a variation of the bifurcation parameters allows us to see that the adjusted model of the neuron eHR is sensitive to the initial conditions, and therefore exhibits the multistability, which is produced by the phenomenon of parallel branches or hysteresis in this system. To control these coexistences of attractors, a control method based on the feedback term is applied to the model.

Results

We see that the addition of this space-dependent feedback term to the dynamic equation of this model drives the dynamic towards the desired attractor by annihilating the other. This powerful technique makes it possible to move from a multistable system to a monostable system.

Conclusion

Finally, we propose an on-board system implementation of this neural circuit using microcontroller technology. This constitutes an important and reliable tool which can best mimic biological neurons.

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Acknowledgements

Jules Tagne Fossi thanks the Faculty of Sciences of the University of Ngaoundéré for its important contribution. Zeric Tabekoueng Njitacke has been supported by the Polish National Science Centre under the Grant OPUS 14 No. 2017/27/B/ST8/01330.

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Author notes

  1. Hélène Carole Edima, Zeric Tabekoueng Njitacke, Florent Feudjio Kemwoue, Joseph Marie Mendimi and Jacques Atangana have contributed equally to this work.

Authors and Affiliations

  1. Laboratory of Energy-Electric and Electronic Systems, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon

    Jules Tagne Fossi & Florent Feudjio Kemwoue

  2. National School of Agro-Industrial Sciences, Food Microbiology and Biotechnology Laboratory, University of Ngaoundéré, Ngaoundéré, Cameroon

    Hélène Carole Edima

  3. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O.Box 63, Buea, Cameroon

    Zeric Tabekoueng Njitacke

  4. Department of Morphological Sciences and Morbid Anatomy, Faculty of Medicine and Biomedical Sciences, Yaoundé, Cameroon

    Joseph Marie Mendimi

  5. Department of Physics, Higher Teacher Training College Yaoundé, University of Yaoundé I, Yaoundé, Cameroon

    Jacques Atangana

  6. Centre d’Excellence Africain des Technologies de l’Information et de la Communication (CETIC) Université de Yaoundé I, Yaoundé, Cameroon

    Jules Tagne Fossi & Florent Feudjio Kemwoue

  7. Department of Automation,Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland

    Zeric Tabekoueng Njitacke

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  1. Jules Tagne Fossi
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Fossi, J.T., Edima, H.C., Njitacke, Z.T. et al. Coexistence of Attractors and Its Control with Selection of a Desired Attractor in a Model of Extended Hindmarsh–Rose Neuron with Nonlinear Smooth Fitting Function: Microcontroller Implementation. J. Vib. Eng. Technol. 10, 2751–2764 (2022). https://doi.org/10.1007/s42417-022-00518-8

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