Convergence and periodicity in a delayed network of neurons with threshold nonlinearity
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Date
2003-05-26
Authors
Guo, Shangjiang
Huang, Lihong
Wu, Jianhong
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Neural networks, Feedback, McCulloch-Pitts nonlinearity, One-dimensional map, Convergence, Periodic solution
Citation
Guo, S., Huang, L., & Wu, J. (2003). Convergence and periodicity in a delayed network of neurons with threshold nonlinearity. <i>Electronic Journal of Differential Equations, 2003</i>(61), pp. 1-14.
Rights
Attribution 4.0 International