Long-range patterns in Hindmarsh-Rose networks

Journal article

Authors / Editors

Tabi, Condrad

Research Areas

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Publication Details

Author list: Eteme AS, Tabi CB, Mohamadou A

Publisher: Elsevier

Place: AMSTERDAM

Publication year: 2017

Journal: Communications in Nonlinear Science and Numerical Simulation (1007-5704)

Journal acronym: COMMUN NONLINEAR SCI

Volume number: 43

Start page: 211

End page: 219

Number of pages: 9

ISSN: 1007-5704

eISSN: 1878-7274

Languages: English-Great Britain (EN-GB)

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Abstract

Long-range diffusive effects are included in a discrete Hindmarsh-Rose neural network. Their impact on the emergence of nonlinear patterns is investigated via the modulational instability. The whole system is first shown to fully reduce to a single nonlinear differential-difference equation, which has plane wave solutions. The stability of such solutions is investigated and regions of instability are found to be importantly influenced by long-range parameters. The analytical results are confirmed through direct numerical simulations, where scattered and chaotic patterns illustrate the long-range effect. Synchronized states are described by quasi-periodic patterns for nearest-neighbor coupling. The external stimulus is also shown to efficiently control strong long-range effects via more regular spatiotemporal patterns. (C) 2016 Elsevier B.V. All rights reserved.

Keywords

neural networks, Wave patterns

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