Multistability in recurrent neural networks

Chang Yuan Cheng; Kuang H. Lin; Chih-Wen Shih

doi:10.1137/050632440

Multistability in recurrent neural networks

Chang Yuan Cheng^*, Kuang H. Lin, Chih-Wen Shih

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

127 Scopus citations

Abstract

Stable stationary solutions correspond to memory capacity in the application of associative memory for neural networks. In this presentation, existence of multiple stable stationary solutions for Hopfield-type neural networks with delay and without delay is investigated. Basins of attraction for these stationary solutions are also estimated. Such a scenario of dynamics is established through formulating parameter conditions based on a geometrical setting. The present theory is demonstrated by two numerical simulations on the Hopfield neural networks with delays.

Original language	English
Pages (from-to)	1301-1320
Number of pages	20
Journal	SIAM Journal on Applied Mathematics
Volume	66
Issue number	4
DOIs	https://doi.org/10.1137/050632440
State	Published - 21 Aug 2006

Keywords

Delay equations
Multistability
Neural network

Access to Document

10.1137/050632440

Fingerprint Dive into the research topics of 'Multistability in recurrent neural networks'. Together they form a unique fingerprint.

Cite this

@article{aaa2281021df4e5fb855d413ee33b406,

title = "Multistability in recurrent neural networks",

abstract = "Stable stationary solutions correspond to memory capacity in the application of associative memory for neural networks. In this presentation, existence of multiple stable stationary solutions for Hopfield-type neural networks with delay and without delay is investigated. Basins of attraction for these stationary solutions are also estimated. Such a scenario of dynamics is established through formulating parameter conditions based on a geometrical setting. The present theory is demonstrated by two numerical simulations on the Hopfield neural networks with delays.",

keywords = "Delay equations, Multistability, Neural network",

author = "Cheng, {Chang Yuan} and Lin, {Kuang H.} and Chih-Wen Shih",

year = "2006",

month = aug,

day = "21",

doi = "10.1137/050632440",

language = "English",

volume = "66",

pages = "1301--1320",

journal = "SIAM Journal on Applied Mathematics",

issn = "0036-1399",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

}

TY - JOUR

T1 - Multistability in recurrent neural networks

AU - Cheng, Chang Yuan

AU - Lin, Kuang H.

AU - Shih, Chih-Wen

PY - 2006/8/21

Y1 - 2006/8/21

N2 - Stable stationary solutions correspond to memory capacity in the application of associative memory for neural networks. In this presentation, existence of multiple stable stationary solutions for Hopfield-type neural networks with delay and without delay is investigated. Basins of attraction for these stationary solutions are also estimated. Such a scenario of dynamics is established through formulating parameter conditions based on a geometrical setting. The present theory is demonstrated by two numerical simulations on the Hopfield neural networks with delays.

AB - Stable stationary solutions correspond to memory capacity in the application of associative memory for neural networks. In this presentation, existence of multiple stable stationary solutions for Hopfield-type neural networks with delay and without delay is investigated. Basins of attraction for these stationary solutions are also estimated. Such a scenario of dynamics is established through formulating parameter conditions based on a geometrical setting. The present theory is demonstrated by two numerical simulations on the Hopfield neural networks with delays.

KW - Delay equations

KW - Multistability

KW - Neural network

UR - http://www.scopus.com/inward/record.url?scp=33747179498&partnerID=8YFLogxK

U2 - 10.1137/050632440

DO - 10.1137/050632440

M3 - Article

AN - SCOPUS:33747179498

VL - 66

SP - 1301

EP - 1320

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 4

ER -

Multistability in recurrent neural networks

Abstract

Keywords

Access to Document

Other files and links

Cite this