Convergent and oscillatory activation dynamics for cascades of neural nets with nearest neighbor competitive or cooperative interactions

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

It is shown that a cascade of the neural net n0 into the net n1 has oscillatory (convergent) dynamics if the nets n0 and n1 have oscillatory (convergent) dynamics and the net n1 has a special structure. The special structure required of n1 is that it consists of a finite number of units which can be arranged along a line segment with only nearest neighbor connections between units and where each adjacent pair of units interacts in either a mutally inhibitory manner or in a mutually excitatory manner. These nets, described in Hirsch (1989), have convergent dynamics if given constant input, by a result of Smillie (1984), and have oscillatory dynamics if given oscillatory input, by a result of the author (1990).

Original languageEnglish (US)
Pages (from-to)41-46
Number of pages6
JournalNeural Networks
Volume4
Issue number1
DOIs
StatePublished - 1991

Fingerprint

Chemical activation
Neural networks

Keywords

  • Cascade
  • Convergent dynamics
  • Oscillatory dynamics
  • Tridiagonal competitive-cooperative systems

ASJC Scopus subject areas

  • Artificial Intelligence
  • Neuroscience(all)

Cite this

@article{7a6fdbff600c4a708e2a15c4fded4098,
title = "Convergent and oscillatory activation dynamics for cascades of neural nets with nearest neighbor competitive or cooperative interactions",
abstract = "It is shown that a cascade of the neural net n0 into the net n1 has oscillatory (convergent) dynamics if the nets n0 and n1 have oscillatory (convergent) dynamics and the net n1 has a special structure. The special structure required of n1 is that it consists of a finite number of units which can be arranged along a line segment with only nearest neighbor connections between units and where each adjacent pair of units interacts in either a mutally inhibitory manner or in a mutually excitatory manner. These nets, described in Hirsch (1989), have convergent dynamics if given constant input, by a result of Smillie (1984), and have oscillatory dynamics if given oscillatory input, by a result of the author (1990).",
keywords = "Cascade, Convergent dynamics, Oscillatory dynamics, Tridiagonal competitive-cooperative systems",
author = "Hal Smith",
year = "1991",
doi = "10.1016/0893-6080(91)90029-5",
language = "English (US)",
volume = "4",
pages = "41--46",
journal = "Neural Networks",
issn = "0893-6080",
publisher = "Elsevier Limited",
number = "1",

}

TY - JOUR

T1 - Convergent and oscillatory activation dynamics for cascades of neural nets with nearest neighbor competitive or cooperative interactions

AU - Smith, Hal

PY - 1991

Y1 - 1991

N2 - It is shown that a cascade of the neural net n0 into the net n1 has oscillatory (convergent) dynamics if the nets n0 and n1 have oscillatory (convergent) dynamics and the net n1 has a special structure. The special structure required of n1 is that it consists of a finite number of units which can be arranged along a line segment with only nearest neighbor connections between units and where each adjacent pair of units interacts in either a mutally inhibitory manner or in a mutually excitatory manner. These nets, described in Hirsch (1989), have convergent dynamics if given constant input, by a result of Smillie (1984), and have oscillatory dynamics if given oscillatory input, by a result of the author (1990).

AB - It is shown that a cascade of the neural net n0 into the net n1 has oscillatory (convergent) dynamics if the nets n0 and n1 have oscillatory (convergent) dynamics and the net n1 has a special structure. The special structure required of n1 is that it consists of a finite number of units which can be arranged along a line segment with only nearest neighbor connections between units and where each adjacent pair of units interacts in either a mutally inhibitory manner or in a mutually excitatory manner. These nets, described in Hirsch (1989), have convergent dynamics if given constant input, by a result of Smillie (1984), and have oscillatory dynamics if given oscillatory input, by a result of the author (1990).

KW - Cascade

KW - Convergent dynamics

KW - Oscillatory dynamics

KW - Tridiagonal competitive-cooperative systems

UR - http://www.scopus.com/inward/record.url?scp=0026064839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026064839&partnerID=8YFLogxK

U2 - 10.1016/0893-6080(91)90029-5

DO - 10.1016/0893-6080(91)90029-5

M3 - Article

AN - SCOPUS:0026064839

VL - 4

SP - 41

EP - 46

JO - Neural Networks

JF - Neural Networks

SN - 0893-6080

IS - 1

ER -