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International Conference: 2004 - Dynamical Systems and Applications
July 5-10, 2004

Antalya, Turkey

Organizers
Akca Haydar, Basem S. Attili, Boucherif Abdelkader, Cho Yeol Je, Covachev Valery, Gyori Istvan, Maksimov Vyacheslav, Stavroulakis Ioannis P.

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Neural networks: Modeling with Impulsive Differential Equations
by
Haydar Akca
King Fahd University of Petroleum and Minerals, Department of Mathematical Science, Dhahran 31261,Saudi Arabia
Coauthors: Rajai Alassar and Shebadeh Mustafa Yaqoub

{\bf Neural networks: Modeling with Impulsive Differential Equations}

Neural networks: Modeling with Impulsive Differential Equations

Haydar Akça1, Rajai Alassar and Shebadeh Mustafa Yaqoub
King Fahd University of Petroleum and Minerals
Department of Mathematical Science
Dhahran 31261, Saudi Arabia

Abstract

Neural networks are models of the brain's cognitive process. The neuron is the basic processor in neural networks. The activation of the neuron is computed by applying a threshold function to this product. This threshold function is generally some form of nonlinear function.

The aim of this work is to investigate and discuss different way to generalize the original Hopfield, McCulloch-Pitts model by making the output of a unit a continuous variable instead of a binary 0 / 1 or -1, +1. This is more realistic for real neurons, sometimes more convenient for analog hardware implementation and in some contexts makes analysis easier. The activation function g(u) is usually nonlinear. In most cases we want it to have a saturation nonlinearity so that g(u) levels off and approaches fixed limits for large negative and positive u. Then the output will always remain between those limits. There are several possible choices for defining the output functions and we will represent by the set of differential equations.

Footnotes:

1Corresponding author. Research partially supported by KFUPM

Date received: May 16, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caoe-35.