Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 4, Pages 313-332
doi:10.1155/S1048953391000242
    
    
    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.
     
    
    
   
 
Abstract
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.