Unstable discrete modes in Hindmarsh–Rose neural networks under magnetic flow effect

Conrad B. Tabi, Armand Sylvin Etémé, Alidou Mohamadou, T. C. Kofané

Research output: Contribution to journalArticle

Abstract

The competitive effect between electric and magnetic flux couplings is used, in the context of modulational instability, to describe the collective dynamics in a modified Hindmarsh–Rose neural networks. The multiple-scale expansion is utilized to reduce the system to a nonlinear differential-difference equation, whose plane wave solutions are found to be unstable for some values of parameters. Particular interest is given to the influence of changing both the electric and magnetic coupling strengths, and confirmation of analytical results is given via numerical integration of the generic Hindmarsh–Rose model. The model presents a rich variety of spatiotemporal patterns propagating in the network, as the result of the interplay between nonlinear and dispersive effects. The electromagnetic induction appears to be responsible for regular bursting patterns and synchronous states in the network. With increasing the electric coupling, full synchronization is difficult to realize and irregular spatiotemporal patterns of action potentials are predominant.
Original languageEnglish
Pages (from-to)116
Number of pages123
JournalChaos, Solitons and Fractals
Volume123
Publication statusPublished - Apr 7 2019

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Spatio-temporal Patterns
Unstable
Neural Networks
Electromagnetic Induction
Modulational Instability
Bursting
Differential-difference Equations
Multiple Scales
Action Potential
Plane Wave
Numerical integration
Irregular
Nonlinear Equations
Synchronization
Model
Context
Influence

Cite this

Tabi, Conrad B. ; Etémé, Armand Sylvin ; Mohamadou, Alidou ; Kofané, T. C. / Unstable discrete modes in Hindmarsh–Rose neural networks under magnetic flow effect. In: Chaos, Solitons and Fractals. 2019 ; Vol. 123. pp. 116.
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Unstable discrete modes in Hindmarsh–Rose neural networks under magnetic flow effect. / Tabi, Conrad B.; Etémé, Armand Sylvin; Mohamadou, Alidou; Kofané, T. C.

In: Chaos, Solitons and Fractals, Vol. 123, 07.04.2019, p. 116.

Research output: Contribution to journalArticle

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