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

Author

Jourjine, Alexander N.

Author_Institution

Wang Lab., Advanced Technology, Lowell, MA, USA

fYear

1993

fDate

6-9 Sep 1993

Firstpage

11

Lastpage

13

Abstract

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

Keywords

Lyapunov methods; bifurcation; integral equations; neural nets; nonlinear equations; transfer functions; Hammerstein equation; Lyapunov function; additive neural networks; bifurcation; nonlinear integral equations; spectral properties; weight matrix symmetric part positivity; Additives; Bifurcation; Integral equations; Laboratories; Lyapunov method; Neural networks; Nonlinear equations; Orbits; Symmetric matrices; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks for Processing [1993] III. Proceedings of the 1993 IEEE-SP Workshop

Conference_Location

Linthicum Heights, MD

Print_ISBN

0-7803-0928-6

Type

conf

DOI

10.1109/NNSP.1993.471889

Filename

471889