Noise-induced complex dynamics and synchronization in the map-based Chialvo neuron model
type: Item
instance of: scholarly article
title: Noise-induced complex dynamics and synchronization in the map-based Chialvo neuron model
zbMATH Open document ID: 1505.92006
author: Lev Ryashko
author: Javier Used
author: Jesús M. Seoane
author: Miguel A. F. Sanjuán
author: Irina Bashkirtseva
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2022-10-28T00:00:00Z
review text: The aim in this article is an experimentally investigation of the neuron activity, actually a numerical study on how noise influences the dynamics of a neural network. As prototype, the quite simple map-based Chialvo neuron model described in the work of \textit{D. R. Chialvo} [Chaos Solitons Fractals 5, No. 3--4, 461--479 (1995; Zbl 0925.92020)], is considered. In the second section of the paper, one introduces the deterministic Chialvo model \[ x_{t+1}={x_t}^2\exp(y_t-x_t)+I \] \[ y_{t+1}=ay_t-bx_t+c \] where \(x\) stands for the activation variable, \(y\) for the recovery, \(I\) models the action of the ion current injected into the neuron and parameter \(a,b,c\) characterize recovery process. For different values of \(a,b,c\) and \(I\), the system behavior is discussed and diagrams are shown. In the third section one extends the investigation to a stochastic model obtained by adding to the first equation of the considered Chialvo model, a noise \(\epsilon\xi_t\). Experiments for different values of \(I\) and the noise intensity \(\epsilon\) are performed, results are plotted, discussed and interpreted. In the fourth section one analyzes the effects of the noise on a two-neurons network. The aim is to study the synchronization between the neurons due to noise effects. The complete model of the network is presented and for different model parameters the time series of both neurons are plotted. Further, in the fifth section, by varying model parameter and noise one obtains numerical evidence for the synchronization process. Conclusions and discussion are to be found in the sixth section.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 7609364
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: map-based neuron models
zbMATH Keywords: noise-induced effects
zbMATH Keywords: neuronal dynamics
zbMATH Keywords: synchronization
MaRDI profile type: Publication
full work available at URL: j.cnsns.2022.106867
OpenAlex ID: W4294723960
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DOI: 10.1016/J.CNSNS.2022.106867
description: scientific article; zbMATH DE number 7609364