On Some Dynamical Properties of Threshold and Homogeneous Networks

Hiromi MIYAJIMA  Shuji YATSUKI  Noritaka SHIGEI  Sadayuki MURASHIMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.11   pp.1823-1830
Publication Date: 1994/11/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
Category: Neural Network and Its Applications
homogeneous networks,  threshold networks,  dynamics,  periodic sequences,  transient sequences,  

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It is known that homogeneous networks are ones which perform parallel algorithms, and the dynamics of neural networks are applied to practical problems including combinatorial optimization problems. Both homogeneous and neural networks are parallel networks, and are composed of Boolean elements. Although a large number of studies have been made on the applications of homogeneous threshold networks, little is known about the relation of the dynamics of these networks. In this paper, some results about the dynamics, used to find the lengths of periodic and transient sequences, as built by parallel networks including threshold and homogeneous networks are shown. First, we will show that for non–restricted parallel networks, threshold networks which permit only two elements to transit at each step, and homogeneous networks, it is possible to build periodic and transient sequences of almost any lengths. Further, it will be shown that it is possible for triangular threshold networks to build periodic and transient sequences with short lengths only. As well, homogeneous threshold networks also seem to build periodic and transient sequences with short lengths only. Specifically, we will show a sufficient condition for symmetric homogeneous threshold networks to have periodic sequences with the length 1.