Hopf bifurcation in a general n-neuron ring network with n time delays

In this paper, we consider a general ring network consisting of n neurons and n time delays. By analyzing the associated characteristic equation, a classification according to n is presented. It is investigated that Hopf bifur-cation occurs when the sum of the n delays passes through a critical valu...

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Main Authors:	Elham Javidmanesh, Mohsen Khorshidi
Format:	Article
Language:	English
Published:	Ferdowsi University of Mashhad 2014-11-01
Series:	Iranian Journal of Numerical Analysis and Optimization
Subjects:	ring network stability periodic solution hopf bifurcation time delay
Online Access:	https://ijnao.um.ac.ir/article_24432_e3ffe80f49324d2ada232629971141b5.pdf

id	doaj-3db72b87778f48ceaa9f4202d9208bc4
record_format	Article
spelling	doaj-3db72b87778f48ceaa9f4202d9208bc42021-06-02T06:40:52ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692014-11-0142153010.22067/ijnao.v4i2.4022724432Hopf bifurcation in a general n-neuron ring network with n time delaysElham Javidmanesh0Mohsen Khorshidi1Ferdowsi University of MashhadFerdowsi University of MashhadIn this paper, we consider a general ring network consisting of n neurons and n time delays. By analyzing the associated characteristic equation, a classification according to n is presented. It is investigated that Hopf bifur-cation occurs when the sum of the n delays passes through a critical value.In fact, a family of periodic solutions bifurcate from the origin, while the zero solution loses its asymptotically stability. To illustrate our theoretical results, numerical simulation is given.https://ijnao.um.ac.ir/article_24432_e3ffe80f49324d2ada232629971141b5.pdfring networkstabilityperiodic solutionhopf bifurcationtime delay
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Elham Javidmanesh Mohsen Khorshidi
spellingShingle	Elham Javidmanesh Mohsen Khorshidi Hopf bifurcation in a general n-neuron ring network with n time delays Iranian Journal of Numerical Analysis and Optimization ring network stability periodic solution hopf bifurcation time delay
author_facet	Elham Javidmanesh Mohsen Khorshidi
author_sort	Elham Javidmanesh
title	Hopf bifurcation in a general n-neuron ring network with n time delays
title_short	Hopf bifurcation in a general n-neuron ring network with n time delays
title_full	Hopf bifurcation in a general n-neuron ring network with n time delays
title_fullStr	Hopf bifurcation in a general n-neuron ring network with n time delays
title_full_unstemmed	Hopf bifurcation in a general n-neuron ring network with n time delays
title_sort	hopf bifurcation in a general n-neuron ring network with n time delays
publisher	Ferdowsi University of Mashhad
series	Iranian Journal of Numerical Analysis and Optimization
issn	2423-6977 2423-6969
publishDate	2014-11-01
description	In this paper, we consider a general ring network consisting of n neurons and n time delays. By analyzing the associated characteristic equation, a classification according to n is presented. It is investigated that Hopf bifur-cation occurs when the sum of the n delays passes through a critical value.In fact, a family of periodic solutions bifurcate from the origin, while the zero solution loses its asymptotically stability. To illustrate our theoretical results, numerical simulation is given.
topic	ring network stability periodic solution hopf bifurcation time delay
url	https://ijnao.um.ac.ir/article_24432_e3ffe80f49324d2ada232629971141b5.pdf
work_keys_str_mv	AT elhamjavidmanesh hopfbifurcationinageneralnneuronringnetworkwithntimedelays AT mohsenkhorshidi hopfbifurcationinageneralnneuronringnetworkwithntimedelays
_version_	1721407579528101888

Hopf bifurcation in a general n-neuron ring network with n time delays

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