Frequency mode excitations in two-dimensional Hindmarsh-Rose neural networks

Journal article

Authors / Editors

Tabi, Condrad

Research Areas

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Publication Details

Author list: Tabi CB, Eteme AS, Mohamadou A

Publisher: Elsevier

Place: AMSTERDAM

Publication year: 2017

Journal: Physica A: Statistical Mechanics and its Applications (0378-4371)

Journal acronym: PHYSICA A

Volume number: 474

Start page: 186

End page: 198

Number of pages: 13

ISSN: 0378-4371

eISSN: 1873-2119

Languages: English-Great Britain (EN-GB)

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Abstract

In this work, we explicitly show the existence of two frequency regimes in a two-dimensional Hindmarsh-Rose neural network. Each of the regimes, through the semi discrete approximation, is shown to be described by a two-dimensional complex Ginzburg-Landau equation. The modulational instability phenomenon for the two regimes is studied, with consideration given to the coupling intensities among neighboring neurons. Analytical solutions are also investigated, along with their propagation in the two frequency regimes. These waves, depending on the coupling strength, are identified as breathers, impulses and trains of soliton-like structures. Although the waves in two regimes appear in some common regions of parameters, some phase differences are noticed and the global dynamics of the system is highly influenced by the values of the coupling terms. For some values of such parameters, the high-frequency regime displays modulated trains of waves, while the low-frequency dynamics keeps the original asymmetric character of action potentials. We argue that in a wide range of pathological situations, strong interactions among neurons can be responsible for some pathological states, including schizophrenia and epilepsy. (C) 2017 Elsevier B.V. All rights reserved.

Keywords

Nerve impulses, neural networks, Wave frequency

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