Dynamics and bifurcations of a discrete time neural network with self connection

Zohreh Eskandari; Javad Alidousti; Zakieh Avazzadeh; Reza Koshsiar Ghaziani

doi:10.1016/j.ejcon.2022.100642

Dynamics and bifurcations of a discrete time neural network with self connection

Zohreh Eskandari^*, Javad Alidousti, Zakieh Avazzadeh, Reza Koshsiar Ghaziani

^*Corresponding author for this work

Department of Applied Mathematics

Shahrekord University

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

This paper investigates the dynamical behavior of a discrete-time neural network system from both analytical and numerical points of view. The conditions as well as the critical coefficients for the pitchfork, flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. Using critical coefficients, the bifurcation scenarios were determined for each bifurcation point. By changing one or two parameters, bifurcation curves of fixed points and cycles with periods up to four iterates, were obtained. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.

Original language	English
Article number	100642
Journal	European Journal of Control
Volume	66
DOIs	https://doi.org/10.1016/j.ejcon.2022.100642
Publication status	Published - Jul 2022

Keywords

Bifurcation
Degenerate bifurcation
Generic bifurcation
Neural network

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10.1016/j.ejcon.2022.100642

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title = "Dynamics and bifurcations of a discrete time neural network with self connection",

abstract = "This paper investigates the dynamical behavior of a discrete-time neural network system from both analytical and numerical points of view. The conditions as well as the critical coefficients for the pitchfork, flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. Using critical coefficients, the bifurcation scenarios were determined for each bifurcation point. By changing one or two parameters, bifurcation curves of fixed points and cycles with periods up to four iterates, were obtained. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.",

keywords = "Bifurcation, Degenerate bifurcation, Generic bifurcation, Neural network",

author = "Zohreh Eskandari and Javad Alidousti and Zakieh Avazzadeh and {Koshsiar Ghaziani}, Reza",

note = "Funding Information: This work is supported by the Shahrekord University of Iran. Compliance with ethical standards, the authors declare that they have no conflict of interest concerning the publication of this manuscript. Publisher Copyright: {\textcopyright} 2022 European Control Association",

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AU - Eskandari, Zohreh

AU - Alidousti, Javad

AU - Avazzadeh, Zakieh

AU - Koshsiar Ghaziani, Reza

N1 - Funding Information: This work is supported by the Shahrekord University of Iran. Compliance with ethical standards, the authors declare that they have no conflict of interest concerning the publication of this manuscript. Publisher Copyright: © 2022 European Control Association

PY - 2022/7

Y1 - 2022/7

N2 - This paper investigates the dynamical behavior of a discrete-time neural network system from both analytical and numerical points of view. The conditions as well as the critical coefficients for the pitchfork, flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. Using critical coefficients, the bifurcation scenarios were determined for each bifurcation point. By changing one or two parameters, bifurcation curves of fixed points and cycles with periods up to four iterates, were obtained. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.

AB - This paper investigates the dynamical behavior of a discrete-time neural network system from both analytical and numerical points of view. The conditions as well as the critical coefficients for the pitchfork, flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. Using critical coefficients, the bifurcation scenarios were determined for each bifurcation point. By changing one or two parameters, bifurcation curves of fixed points and cycles with periods up to four iterates, were obtained. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.

KW - Bifurcation

KW - Degenerate bifurcation

KW - Generic bifurcation

KW - Neural network

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DO - 10.1016/j.ejcon.2022.100642

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SN - 0947-3580

VL - 66

JO - European Journal of Control

JF - European Journal of Control

M1 - 100642

ER -

Dynamics and bifurcations of a discrete time neural network with self connection

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Keywords

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