Analysis of neural networks with time-delays using the Lambert W function

Neural networks have been used in various areas. In the implementation of the networks, time-delays and uncertainty are present, and induce complex behaviors. In this paper, stability and robust stability of neural networks considering time-delays and parametric uncertainty is investigated. For stability analysis, the dominant characteristic roots are obtained by using an approach based on the Lambert W function. The Lambert W function has already embedded in various commercial software packages (e.g., Matlab, Maple, and Mathematica). In a way similar to non-delay systems, stability is determined with the locations of the characteristic roots in the complex plane. Conditions for oscillation and robust stability are also given in term of the Lambert W function. Numerical examples are provided and the results are compared to existing approaches (e.g., bifurcation method) and discussed.