Long-range patterns in Hindmarsh–Rose networks

Armand Sylvin Etémé, Conrad Bertrand Tabi, Alidou Mohamadou

Research output: Contribution to journalArticle

18 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)211-219
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume43
DOIs
Publication statusPublished - Feb 1 2017

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Range of data
Direct numerical simulation
Difference equations
Modulational Instability
Spatio-temporal Patterns
Differential-difference Equations
Stability of Solutions
Plane Wave
Neural networks
Nearest Neighbor
Nonlinear Equations
Neural Networks
Direct numerical Simulation

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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Long-range patterns in Hindmarsh–Rose networks. / Etémé, Armand Sylvin; Tabi, Conrad Bertrand; Mohamadou, Alidou.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 43, 01.02.2017, p. 211-219.

Research output: Contribution to journalArticle

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