Analysis and synthesis of a class of neural networks: linear systems operating on a closed hypercube

Author

Li, Jian-Hua ; Michel, Anthony N. ; Porod, Wolfgang

Author_Institution

Dept. of Electr. & Comput. Eng., Notre Dame Univ., IN, USA

Volume

36

Issue

11

fYear

1989

fDate

11/1/1989 12:00:00 AM

Firstpage

1405

Lastpage

1422

Abstract

An investigation was conducted of the qualitative properties of a class of neural networks described by a system of first-order linear ordinary differential equations which are defined on a closed hypercube of the state space with solutions extended to the boundary of the hypercube. When solutions are located on the boundary of the hypercube, the system is said to be in a saturated mode. The class of systems considered retains the basic structure of the Hopfield model but is easier to analyze, synthesize, and implement. An efficient analysis method is developed which can be used to determine completely the set of asymptotically stable equilibrium points and the set of unstable equilibrium points. The latter set can be used to estimate the domains of attraction for the elements of the former set. The class of systems considered can easily be implemented in analog integrated circuits. The applicability of the results is demonstrated by means of several examples

Keywords

analogue circuits; linear differential equations; linear systems; neural nets; state-space methods; Hopfield model; analog integrated circuits; asymptotically stable equilibrium points; closed hypercube; first-order linear ordinary differential equations; neural networks; saturated mode; state space; unstable equilibrium points; Analog integrated circuits; Differential equations; Hypercubes; Integrated circuit synthesis; Linear systems; Network synthesis; Neural networks; State-space methods; Vectors; Very large scale integration;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.41297

Filename

41297