Monthly
288 pp. per issue
6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

September 1992, Vol. 4, No. 5, Pages 621-642
(doi: 10.1162/neco.1992.4.5.621)
© 1992 Massachusetts Institute of Technology
Nonlinear Dynamics and Symbolic Dynamics of Neural Networks
Article PDF (954.24 KB)
Abstract

A piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks. A symbolic representation of the dynamics in this equation is given as a directed graph on an N-dimensional hypercube. This provides a formal link with discrete neural networks such as the original Hopfield models. Analytic criteria are given to establish steady states and limit cycle oscillations independent of network dimension. Model networks that display multiple stable limit cycles and chaotic dynamics are discussed. The results show that such equations are a useful and efficient method of investigating the behavior of neural networks.