IJPAM: Volume 2, No. 2 (2002)

CHAOTIC PROPERTIES OF NEURAL
NETWORKS: CHAOTIC RESPONSE OF
RMS SERIES AND EFFECTS ON THE
ABSOLUTE ERROR DISTRIBUTION

Nikos Kofidis$^1$, Manos Roumeliotis$^2$, Miltiadis Adamopoulos$^3$
Dept. of Applied Informatics, Economic and Social Sciences
University of Macedonia, P.O. Box 1591, Egnatia 156
Thessaloniki 54006, GREECE
$^1$e-mail: kofid@uom.gr
$^2$e-mail: manos@uom.gr
$^3$e-mail: miltos@uom.gr


Abstract.This paper investigates chaotic properties of neural models of the chaotic attractors of the logistic and Henon maps, to determine efficient training strategies. Specifically, series of the RMS error are submitted to Lyapunov exponent investigation in a two-phase process. At first the networks are trained for different initial values of the weight vector, and then, the best and the worst of the resulting networks are submitted to additional training. In both cases, the Dominant Lyapunov Exponent is calculated for the RMS series of the training set. The positive value of the exponent implies the chaotic response of the RMS. To make final conclusions for the chaotic response of the error the stability, the performance of the calculated exponents is investigated. Although the RMS attractor is narrow, it seems to have significant effects in the resulting level of the absolute error, which strongly affects the actual response of the neural model.

Received: April 22, 2002

AMS Subject Classification: 65P20

Key Words and Phrases: chaos theory and models, neural networks, nonlinear dynamical systems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 2