Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 4, Pages 313-332
Neural networks with memory
Southern Illinois University, Department of Mathematics, Carbondale 62901-4408, Illinois, USA
Received 1 April 1991; Revised 1 August 1991
Copyright © 1991 T. A. Burton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is divided into four parts. Part 1 contains a survey of
three neural networks found in the literature and which motivate this
work. In Part 2 we model a neural network with a very general integral
form of memory, prove a boundedness result, and obtain a first result on
asymptotic stability of equilibrium points. The system is very general
and we do not solve the stability problem. In the third section we show
that the neural networks are very robust. The fourth section concerns
simplification of the systems from the second part. Several asymptotic
stability results are obtained for the simplified systems.