Long-range memory effects in a magnetized Hindmarsh-Rose neural network

Armand S. Etémé, Conrad B. Tabi, Alidou Mohamadou, Timoléon C. Kofané

Research output: Contribution to journalArticle

Abstract

We consider a model network of diffusively coupled Hindmarsh-Rose neurons to study both analytically and numerically, long-range memory effects on the modulational instability phenomenon, chaotic, synchronous and chimera states within the network. The multiple scale method is used to reduce the generic model into a discrete nonlinear Schrödinger equation. The latter is explored in the linear stability analysis and the instability criterion along with the critical amplitude are derived. The analytical results predict that strong local coupling, high electromagnetic induction and strong long-range interactions may support the formation of highly localized excitations in neural networks. Through numerical simulations, the largest Lyapunov exponents are computed for studying chaos, the synchronization factor and the strong of incoherence are recorded for studying, respectively synchronous and chimera states in the network. We find the appropriate domains of space parameters where these rich activities could be observed. As a result, quasi-periodic synchronous patterns, chaotic chimera and synchronous states, strange chaotic and non-chaotic attractors are found to be the main features of membrane potential coupled with memristive current during long-range memory activities of neural networks. Our results suggest that a combination of long-range activity and memory effects in neural networks may produces a rich variety of membrane potential patterns which are involved in information processing, odors recognition and discrimination and various diseases in the brain.

Original languageEnglish
Article number105208
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume84
DOIs
Publication statusPublished - May 2020

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Memory Effect
Membrane Potential
Neural Networks
Neural networks
Data storage equipment
Range of data
Electromagnetic Induction
Multiple Scales Method
Membranes
Modulational Instability
Largest Lyapunov Exponent
Linear stability analysis
Electromagnetic induction
Long-range Interactions
Linear Stability Analysis
Odors
Discrete Equations
Information Processing
Nonlinear equations
Chaos theory

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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abstract = "We consider a model network of diffusively coupled Hindmarsh-Rose neurons to study both analytically and numerically, long-range memory effects on the modulational instability phenomenon, chaotic, synchronous and chimera states within the network. The multiple scale method is used to reduce the generic model into a discrete nonlinear Schr{\"o}dinger equation. The latter is explored in the linear stability analysis and the instability criterion along with the critical amplitude are derived. The analytical results predict that strong local coupling, high electromagnetic induction and strong long-range interactions may support the formation of highly localized excitations in neural networks. Through numerical simulations, the largest Lyapunov exponents are computed for studying chaos, the synchronization factor and the strong of incoherence are recorded for studying, respectively synchronous and chimera states in the network. We find the appropriate domains of space parameters where these rich activities could be observed. As a result, quasi-periodic synchronous patterns, chaotic chimera and synchronous states, strange chaotic and non-chaotic attractors are found to be the main features of membrane potential coupled with memristive current during long-range memory activities of neural networks. Our results suggest that a combination of long-range activity and memory effects in neural networks may produces a rich variety of membrane potential patterns which are involved in information processing, odors recognition and discrimination and various diseases in the brain.",
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Long-range memory effects in a magnetized Hindmarsh-Rose neural network. / Etémé, Armand S.; Tabi, Conrad B.; Mohamadou, Alidou; Kofané, Timoléon C.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 84, 105208, 05.2020.

Research output: Contribution to journalArticle

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AU - Mohamadou, Alidou

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