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Phase synchronization, extreme multistability and its control with selection of a desired pattern in hybrid coupled neurons via a memristive synapse

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Abstract

The memristor is a nonlinear electronic nanodevice with incredible biomimetic characteristics generally used by neurologists, more specifically in neuromorphics, to design artificial neural systems, also called memristive neuron networks. In this manuscript, a photosensitive FitzHugh–Nagumo neuron (FHN) model and a thermosensitive FHN neuron model coupled via a memristive synapse with a sinus memductance are presented. Basic traditional methods of analysis of nonlinear systems have been used to demonstrate that the coupled neurons exhibit periodic and chaotic bursting behaviors under the influence of light. Phenomena of extreme homogeneous and heterogeneous multistability can be observed when the internal memristor state variable changes periodically. It is also reported that the model can achieve phase synchronization stability as the coupling strength increases. A feedback term dependent on a dynamic state variable of the coupled neurons is introduced to switch the model from an extreme multistable state to a monostable state. This control technique eliminates all undesired patterns among the coexisting ones. Finally, electronic circuit simulations of the memristive neuron system are performed by Pspice to confirm the numerical results.

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Acknowledgements

Jules Fossi Tagne 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. Vandi Deli, Zeric Tabekoueng Njitacke, Joseph Marie Mendimi, Florent Feudjio Kemwoue and Jacques Atangana 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. Department of Pharmaceutical Sciences, Faculty of Medicine and Pharmaceutical Sciences, University of Douala, Douala, Cameroon

    Vandi Deli

  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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Correspondence to Jules Tagne Fossi or Jacques Atangana.

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Fossi, J.T., Deli, V., Njitacke, Z.T. et al. Phase synchronization, extreme multistability and its control with selection of a desired pattern in hybrid coupled neurons via a memristive synapse. Nonlinear Dyn 109, 925–942 (2022). https://doi.org/10.1007/s11071-022-07489-1

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