A Lyapunov function for additive neural networks and nonlinear integral equations of Hammerstein type

摘要

Using the properties of the nonlinear integral equations of the Hammerstein type, a new Lyapunov function for additive neural networks is constructed. The function does not require monotonicity of the transfer function as does the previously discovered Lyapunov function for the additive networks. Instead positivity of the symmetric part of the weight matrix is required. The results on the Hammerstein equation also allow one to provide simple criteria for estimation of the number of fixed points and their bifurcation. The criteria combine the spectral properties of the weight matrix and the growth properties of the transfer function.