Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions

Author

Yi, Zhang ; Tan, Kok Kiong

Author_Institution

Sch. of Comput. Sci. & Eng., Univ. of Electron. Sci. & Technol. of China, Chengdu, China

Volume

15

Issue

2

fYear

2004

fDate

3/1/2004 12:00:00 AM

Firstpage

329

Lastpage

336

Abstract

This paper studies the multistability of a class of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions. It addresses the nondivergence, global attractivity, and complete stability of the networks. Using the local inhibition, conditions for nondivergence are derived, which not only guarantee nondivergence, but also allow for the existence of multiequilibrium points. Under these nondivergence conditions, global attractive compact sets are obtained. Complete stability is studied via constructing novel energy functions and using the well-known Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.

Keywords

discrete time systems; piecewise linear techniques; recurrent neural nets; stability; transfer functions; Cauchy convergence principle; complete stability; discrete-time network; energy function; multistability; nondivergence condition; piecewise linear activation function; recurrent neural network; Biological neural networks; Computer simulation; Convergence; Digital simulation; Neural network hardware; Neural networks; Neurons; Piecewise linear techniques; Recurrent neural networks; Stability; Linear Models; Neural Networks (Computer); Time Factors;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/TNN.2004.824272

Filename

1288237