Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions

Armand S. Etémé, Conrad B. Tabi, Alidou Mohamadou

Research output: Chapter in Book/Report/Conference proceedingChapter

11 Citations (Scopus)

Abstract

Two electrically coupled Hindmarsh–Rose neural networks are considered, each including power-law long-range dispersive interactions. The whole dynamics of the system is reduced to a set of two coupled complex Ginzburg–Landau equations. The linear stability analysis of the plane wave solutions brings about the existence of two dynamical regimes that predict direct and indirect synchronization of the two networks, under the activation of modulational instability. The conditions for the latter to develop are discussed and used to observe numerically the synchronized longtime dynamics of action potentials, under the effect of both long-range intra-coupling and electrical inter-coupling parameters. Mainly, the synchronization criterion depends on the plane wave amplitudes and for some of their values, perfect and partial inter-network synchronization phenomena are observed. It is also found that indirect synchronization between adjacent networks requires local synchronization among neurons of the same fiber. This is discussed based on some further formulation of the synchronization error, additionally to the time series of action potentials. Some spatiotemporal behaviors of the corresponding bursts of spikes are also discussed using coupling parameters.
Original languageEnglish
Title of host publicationChaos, Solitons and Fractals
PublisherElsevier Ltd
Pages813-826
Number of pages14
Volume104
ISBN (Print)0960-0779
DOIs
Publication statusPublished - Nov 1 2017

Publication series

NameChaos, Solitons and Fractals
Volume104

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synchronism
interactions
plane waves
neurons
spikes
bursts
activation
formulations
fibers

Cite this

Etémé, A. S., Tabi, C. B., & Mohamadou, A. (2017). Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions. In Chaos, Solitons and Fractals (Vol. 104, pp. 813-826). (Chaos, Solitons and Fractals; Vol. 104). Elsevier Ltd. https://doi.org/10.1016/j.chaos.2017.09.037
Etémé, Armand S. ; Tabi, Conrad B. ; Mohamadou, Alidou. / Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions. Chaos, Solitons and Fractals. Vol. 104 Elsevier Ltd, 2017. pp. 813-826 (Chaos, Solitons and Fractals).
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Etémé, AS, Tabi, CB & Mohamadou, A 2017, Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions. in Chaos, Solitons and Fractals. vol. 104, Chaos, Solitons and Fractals, vol. 104, Elsevier Ltd, pp. 813-826. https://doi.org/10.1016/j.chaos.2017.09.037

Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions. / Etémé, Armand S.; Tabi, Conrad B.; Mohamadou, Alidou.

Chaos, Solitons and Fractals. Vol. 104 Elsevier Ltd, 2017. p. 813-826 (Chaos, Solitons and Fractals; Vol. 104).

Research output: Chapter in Book/Report/Conference proceedingChapter

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AB - Two electrically coupled Hindmarsh–Rose neural networks are considered, each including power-law long-range dispersive interactions. The whole dynamics of the system is reduced to a set of two coupled complex Ginzburg–Landau equations. The linear stability analysis of the plane wave solutions brings about the existence of two dynamical regimes that predict direct and indirect synchronization of the two networks, under the activation of modulational instability. The conditions for the latter to develop are discussed and used to observe numerically the synchronized longtime dynamics of action potentials, under the effect of both long-range intra-coupling and electrical inter-coupling parameters. Mainly, the synchronization criterion depends on the plane wave amplitudes and for some of their values, perfect and partial inter-network synchronization phenomena are observed. It is also found that indirect synchronization between adjacent networks requires local synchronization among neurons of the same fiber. This is discussed based on some further formulation of the synchronization error, additionally to the time series of action potentials. Some spatiotemporal behaviors of the corresponding bursts of spikes are also discussed using coupling parameters.

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Etémé AS, Tabi CB, Mohamadou A. Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions. In Chaos, Solitons and Fractals. Vol. 104. Elsevier Ltd. 2017. p. 813-826. (Chaos, Solitons and Fractals). https://doi.org/10.1016/j.chaos.2017.09.037