Behaviour of Solutions of a Neuron Model

Aija Aņisimova; Inese Bula

doi:10.1007/978-3-030-70795-8_5

Behaviour of Solutions of a Neuron Model

Aija Aņisimova
, Inese Bula

University of Latvia

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › Research › peer-review

Abstract

We consider a discrete-time network of a single neuron as the discrete dynamical system 1xn+1=βxn-g(xn),n=0,1,…, where β> 1 and an internal decay rate, g is a step signal function given by a piecewise constant function which consists of five steps in the form 2. The considered model is quite simple as a mathematical expression, but with complex dynamics of its solutions. The model is highly sensitive to initial conditions and parameters. Small differences in an initial value and parameters yield widely diverging outcomes for the model, giving a great amount of different periodic orbits. Periodic orbits have been discussed according to the different rage of β. We can find some values of parameters such our considered model has the chaotic behaviour.

Original language	English
Title of host publication	13th Chaotic Modeling and Simulation International Conference
Editors	Christos H. Skiadas, Yiannis Dimotikalis
Place of Publication	Cham
Publisher	Springer
Pages	55-72
Number of pages	18
ISBN (Print)	9783030707941
DOIs	https://doi.org/10.1007/978-3-030-70795-8_5
Publication status	Published - 2021

Publication series

Name	Springer Proceedings in Complexity
ISSN (Print)	2213-8684
ISSN (Electronic)	2213-8692

OECD Field of Science

1.1 Mathematics

Keywords

Chaotic maps
Discrete dynamical system
Nonlinear difference equation
Periodic orbits

Access to Document

10.1007/978-3-030-70795-8_5

Cite this

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title = "Behaviour of Solutions of a Neuron Model",

abstract = "We consider a discrete-time network of a single neuron as the discrete dynamical system 1xn+1=βxn-g(xn),n=0,1,…, where β> 1 and an internal decay rate, g is a step signal function given by a piecewise constant function which consists of five steps in the form 2. The considered model is quite simple as a mathematical expression, but with complex dynamics of its solutions. The model is highly sensitive to initial conditions and parameters. Small differences in an initial value and parameters yield widely diverging outcomes for the model, giving a great amount of different periodic orbits. Periodic orbits have been discussed according to the different rage of β. We can find some values of parameters such our considered model has the chaotic behaviour.",

keywords = "Chaotic maps, Discrete dynamical system, Nonlinear difference equation, Periodic orbits",

author = "Aija Aņisimova and Inese Bula",

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year = "2021",

doi = "10.1007/978-3-030-70795-8\_5",

language = "English",

isbn = "9783030707941",

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TY - GEN

T1 - Behaviour of Solutions of a Neuron Model

AU - Aņisimova, Aija

AU - Bula, Inese

PY - 2021

Y1 - 2021

N2 - We consider a discrete-time network of a single neuron as the discrete dynamical system 1xn+1=βxn-g(xn),n=0,1,…, where β> 1 and an internal decay rate, g is a step signal function given by a piecewise constant function which consists of five steps in the form 2. The considered model is quite simple as a mathematical expression, but with complex dynamics of its solutions. The model is highly sensitive to initial conditions and parameters. Small differences in an initial value and parameters yield widely diverging outcomes for the model, giving a great amount of different periodic orbits. Periodic orbits have been discussed according to the different rage of β. We can find some values of parameters such our considered model has the chaotic behaviour.

AB - We consider a discrete-time network of a single neuron as the discrete dynamical system 1xn+1=βxn-g(xn),n=0,1,…, where β> 1 and an internal decay rate, g is a step signal function given by a piecewise constant function which consists of five steps in the form 2. The considered model is quite simple as a mathematical expression, but with complex dynamics of its solutions. The model is highly sensitive to initial conditions and parameters. Small differences in an initial value and parameters yield widely diverging outcomes for the model, giving a great amount of different periodic orbits. Periodic orbits have been discussed according to the different rage of β. We can find some values of parameters such our considered model has the chaotic behaviour.

KW - Chaotic maps

KW - Discrete dynamical system

KW - Nonlinear difference equation

KW - Periodic orbits

UR - https://link.springer.com/chapter/10.1007/978-3-030-70795-8_5

UR - https://www.scopus.com/pages/publications/85122018007

U2 - 10.1007/978-3-030-70795-8_5

DO - 10.1007/978-3-030-70795-8_5

M3 - Conference paper

SN - 9783030707941

T3 - Springer Proceedings in Complexity

SP - 55

EP - 72

BT - 13th Chaotic Modeling and Simulation International Conference

A2 - Skiadas, Christos H.

A2 - Dimotikalis, Yiannis

PB - Springer

CY - Cham

ER -

Behaviour of Solutions of a Neuron Model

Abstract

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Keywords

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