Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 61, pp. 1-14.
Title: Convergence and periodicity in a delayed network of neurons
with threshold nonlinearity
Authors: Shangjiang Guo (Hunan Univ., Changsha, China)
Lihong Huang (Hunan Univ., Changsha, China)
Jianhong Wu (York Univ., Toronto, Ontario, Canada)
Abstract:
We consider an artificial neural network where the signal
transmission is of a digital (McCulloch-Pitts) nature and is
delayed due to the finite switching speed of neurons (amplifiers).
The discontinuity of the signal transmission functions, however,
makes it difficult to apply the existing dynamical systems theory
which usually requires continuity and smoothness. Moreover,
observe that the dynamics of the network completely depends on the
connection weights, we distinguish several cases to discuss the
behaviors of their solutions. We show that the dynamics of the
model can be understood in terms of the iterations of a
one-dimensional map. As, a result, we present a detailed analysis
of the dynamics of the network starting from non-oscillatory
states and show how the connection topology and synaptic weights
determine the rich dynamics.
Submitted June 30, 2002. Revised January 23, 2003. Published May 26, 2003.
Math Subject Classifications: 34K25, 34K13, 92B20.
Key Words: Neural networks; feedback; McCulloch-Pitts nonlinearity;
one-dimensional map; convergence; periodic solution.