Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 4, Pages 313-332

Neural networks with memory

T. A. Burton

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.