Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay

Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay

A distributed delay model of a class of three-neuron network has been investigated. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. A closed interval for a parameter of the system is identified in which Hopf-bifurcating periodic...

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Main Authors: P. D. Gupta, N. C. Majee, A. B. Roy
Format: Article
Language:English
Published: Vilnius University Press 2008-01-01
Series:Nonlinear Analysis
Subjects:
distributed delay
orbital stability
supercritical Hopf-bifurcation
snake of orbits
Online Access:http://www.journals.vu.lt/nonlinear-analysis/article/view/14586
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spelling doaj-3b19f69145dc4e188d1204e5dd1ec2e92020-11-24T23:51:55ZengVilnius University PressNonlinear Analysis1392-51132335-89632008-01-0113110.15388/NA.2008.13.1.14586Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed DelayP. D. Gupta0N. C. Majee1A. B. Roy2Jadavpur University, IndiaJadavpur University, IndiaJadavpur University, India A distributed delay model of a class of three-neuron network has been investigated. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. A closed interval for a parameter of the system is identified in which Hopf-bifurcating periodic solution occurs for each point of such interval. The orbital stability of such bifurcating periodic solution at the extreme points of the interval is ascertained. Lastly global bifurcation aspect of such periodic solutions is studied. The results are illustrated by numerical simulations. http://www.journals.vu.lt/nonlinear-analysis/article/view/14586distributed delayorbital stabilitysupercritical Hopf-bifurcationsnake of orbits
collection DOAJ
language English
format Article
sources DOAJ
author P. D. Gupta
N. C. Majee
A. B. Roy
spellingShingle P. D. Gupta
N. C. Majee
A. B. Roy
Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay
Nonlinear Analysis
distributed delay
orbital stability
supercritical Hopf-bifurcation
snake of orbits
author_facet P. D. Gupta
N. C. Majee
A. B. Roy
author_sort P. D. Gupta
title Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay
title_short Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay
title_full Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay
title_fullStr Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay
title_full_unstemmed Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay
title_sort asymptotic stability, orbital stability of hopf-bifurcating periodic solution of a simple three-neuron artificial neural network with distributed delay
publisher Vilnius University Press
series Nonlinear Analysis
issn 1392-5113
2335-8963
publishDate 2008-01-01
description A distributed delay model of a class of three-neuron network has been investigated. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. A closed interval for a parameter of the system is identified in which Hopf-bifurcating periodic solution occurs for each point of such interval. The orbital stability of such bifurcating periodic solution at the extreme points of the interval is ascertained. Lastly global bifurcation aspect of such periodic solutions is studied. The results are illustrated by numerical simulations.
topic distributed delay
orbital stability
supercritical Hopf-bifurcation
snake of orbits
url http://www.journals.vu.lt/nonlinear-analysis/article/view/14586
work_keys_str_mv AT pdgupta asymptoticstabilityorbitalstabilityofhopfbifurcatingperiodicsolutionofasimplethreeneuronartificialneuralnetworkwithdistributeddelay
AT ncmajee asymptoticstabilityorbitalstabilityofhopfbifurcatingperiodicsolutionofasimplethreeneuronartificialneuralnetworkwithdistributeddelay
AT abroy asymptoticstabilityorbitalstabilityofhopfbifurcatingperiodicsolutionofasimplethreeneuronartificialneuralnetworkwithdistributeddelay
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