Electron. J. Diff. Eqns., Vol. 2003(2003), No. 61, pp. 114.
Convergence and periodicity in a delayed network of neurons
with threshold nonlinearity
Shangjiang Guo, Lihong Huang, & Jianhong Wu
Abstract:
We consider an artificial neural network where the signal
transmission is of a digital (McCullochPitts) 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
onedimensional map. As, a result, we present a detailed analysis
of the dynamics of the network starting from nonoscillatory
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, McCullochPitts nonlinearity,
onedimensional map, convergence, periodic solution.
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Shangjiang Guo
College of Mathematics and Econometrics
Hunan University
Changsha, Hunan 410082, China
email: shangjguo@etang.com 

Lihong Huang
College of Mathematics and Econometrics
Hunan University
Changsha, Hunan 410082, China
email: llhuang@hnu.net.cn 

Jianhong Wu
Department of Mathematics and Statistics
York University
Toronto, Ontario, M3J 1P3, Canada
email: wujh@mathstat.yorku.ca 
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