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Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design

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An Erratum to this article was published on 11 February 2017

Abstract

In this paper, we report on the synchronization of a pacemaker neuronal ensemble constituted of an AB neuron electrically coupled to two PD neurons. By the virtue of this electrical coupling, they can fire synchronous bursts of action potential. An external master neuron is used to induce to the whole system the desired dynamics, via a nonlinear controller. Such controller is obtained by a combination of sliding mode and feedback control. The proposed controller is able to offset uncertainties in the synchronized systems. We show how noise affects the synchronization of the pacemaker neuronal ensemble, and briefly discuss its potential benefits in our synchronization scheme. An extended Hindmarsh–Rose neuronal model is used to represent a single cell dynamic of the network. Numerical simulations and Pspice implementation of the synchronization scheme are presented. We found that, the proposed controller reduces the stochastic resonance of the network when its gain increases.

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Acknowledgments

MNEB thanks the Abdus Salam International Centre for Theoretical Physics for hospitality.

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Authors and Affiliations

  1. Laboratory of Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, P. O. Box 067, Dschang, Cameroon

    Elie Bertrand Megam Ngouonkadi, Hilaire Bertrand Fotsin, Martial Kabong Nono & Patrick Herve Louodop Fotso

  2. Instituto de Física Teórica, Universidade Estadual Paulista, UNESP, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, São Paulo, 01140-070, Brazil

    Patrick Herve Louodop Fotso

Authors
  1. Elie Bertrand Megam Ngouonkadi
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  2. Hilaire Bertrand Fotsin
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  3. Martial Kabong Nono
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  4. Patrick Herve Louodop Fotso
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Corresponding author

Correspondence to Hilaire Bertrand Fotsin.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s11571-016-9421-1.

Appendices

Appendix 1: Some mathematical expressions

Here we investigate some mathematical expressions obtained during the application of the Kirchhoff law. First, we give the system parameters as a function of the components of circuits presented in Figs. 5b and 6. These equivalences are given in Table 1

Table 1 Coupled system parameters and their electronic equivalents
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Appendix 2: Electronics components and their used values

Furthermore, the values of resistors and capacitors used in different circuits are given in the Table 2 below.

Table 2 Electronics components and their used values
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Megam Ngouonkadi, E.B., Fotsin, H.B., Kabong Nono, M. et al. Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design. Cogn Neurodyn 10, 385–404 (2016). https://doi.org/10.1007/s11571-016-9393-1

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