Research Article Open Access

Analysis of Time-Delayed Neural Networks via Rightmost Eigenvalue Positions

Sun Yi1, Sangseok Yu2, Jung H. Kim1 and Taher M. Abu-Lebdeh1
  • 1 North Carolina A&T State University, USA
  • 2 Chungnam National University, South Korea
American Journal of Engineering and Applied Sciences
Volume 8 No. 1, 2015, 1-10

DOI: https://doi.org/10.3844/ajeassp.2015.1.10

Submitted On: 27 November 2014 Published On: 26 January 2015

How to Cite: Yi, S., Yu, S., Kim, J. H. & Abu-Lebdeh, T. M. (2015). Analysis of Time-Delayed Neural Networks via Rightmost Eigenvalue Positions. American Journal of Engineering and Applied Sciences, 8(1), 1-10. https://doi.org/10.3844/ajeassp.2015.1.10

Abstract

Neural networks have been frequently used in various areas. In the implementation of the networks, time delays and uncertainty are present and known to lead to complex behaviors, which are hard to predict using classical analysis methods. In this study, stability and robust stability of neural networks considering time delays and parametric uncertainty is studied. For stability analysis, the rightmost eigenvalues (or dominant characteristic roots) are obtained by using an approach based on the Lambert W function. The Lambert W function has already been embedded in various commercial software packages (e.g., MATLAB, Maple and Mathematica). In a way similar to non-delayed systems, stability is determined from the positions of the characteristic roots in the complex plane. Conditions for oscillation and robust stability are also given. Numerical examples are provided and the results are compared to existing approaches (e.g., bifurcation method) and discussed.

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Keywords

  • Neural Network
  • Lambert W Function
  • Eigenvalues Stability
  • Parametric Uncertainty