Open AccessLocalized nonlinear excitations in diffusive memristor-based neuronal networks
Author(s) -
Alain Sylvain Tankou Tagne,
Clovis Ntahkie Takembo,
H. G. Ben-Bolie,
P. Owona Ateba
Publication year - 2019
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0214989
Subject(s) - physics , nonlinear system , electromagnetic field , amplitude , electromagnetic radiation , coupling (piping) , ordinary differential equation , differential equation , perturbation (astronomy) , classical mechanics , statistical physics , topology (electrical circuits) , quantum mechanics , mathematics , mechanical engineering , combinatorics , engineering
We extend the existing ordinary differential equations modeling neural electrical activity to include the memory effect of electromagnetic induction through magnetic flux, used to describe time varying electromagnetic field. Through the multi-scale expansion in the semi-discrete approximation, we show that the neural network dynamical equations can be governed by the complex Ginzburg-Landau equation. The analytical and numerical envelop soliton of this equation are reported. The results obtained suggest the possibility of collective information processing and sharing in the nervous system, operating in both the spatial and temporal domains in the form of localized modulated waves. The effects of memristive synaptic electromagnetic induction coupling and perturbation on the modulated action potential dynamics examined. Large electromagnetic induction coupling strength may contribute to signal block as the amplitude of modulated waves are observed to decrease. This could help in the development of a chemical brain anaesthesia for some brain pathologies.