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Reseach Article

Hopfield Model of a Neuron Action under Dynamical Thresholds

by A.K. Verma, Ruby Khan
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 19 - Number 6
Year of Publication: 2011
Authors: A.K. Verma, Ruby Khan

A.K. Verma, Ruby Khan . Hopfield Model of a Neuron Action under Dynamical Thresholds. International Journal of Computer Applications. 19, 6 ( April 2011), 30-35. DOI=10.5120/2364-3105

@article{ 10.5120/2364-3105,
author = { A.K. Verma, Ruby Khan },
title = { Hopfield Model of a Neuron Action under Dynamical Thresholds },
journal = { International Journal of Computer Applications },
issue_date = { April 2011 },
volume = { 19 },
number = { 6 },
month = { April },
year = { 2011 },
issn = { 0975-8887 },
pages = { 30-35 },
numpages = {9},
url = { },
doi = { 10.5120/2364-3105 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
%0 Journal Article
%1 2024-02-06T20:06:18.515353+05:30
%A A.K. Verma
%A Ruby Khan
%T Hopfield Model of a Neuron Action under Dynamical Thresholds
%J International Journal of Computer Applications
%@ 0975-8887
%V 19
%N 6
%P 30-35
%D 2011
%I Foundation of Computer Science (FCS), NY, USA

In this paper we present Hopfield model of a neuron dynamics given by the neuronic equation. In the first model second order neuronic equation describe the behavior of a neuron in the presence of some local positive feedback. The second model portray two neurons in which first order neuronic equation represents dynamics of the second neuron in the presence of a discharged pulse coded signal function from the first neuron. We have shown that the solution is bounded and the paths surrounding the equilibrium point are not closed curves in the phase plane. Some conditions ensuring the existence and uniqueness of the equilibrium point are derived.

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Index Terms

Computer Science
Information Sciences


Dynamical thresholds Equilibrium point Convergence Lyapunov functional Homotopic mapping Homotopy invariance principle Bendixson's criteria Limit cycles