Global Stability of Some Classes of Neural Networks
Summary :
Global stability of equilibrium states is investigated for a continuous-time model of neural networks and a discrete-time one. Three classes of globally stable networks are introduced. One class called weakly coupled networks is shown to be globally asymptotically stable, i.e. every trajectory eventually converges to a unique equilibrium point. The other two classes of which one is called gradient networks and the other is called type K monotone networks are guaranteed to be completely stable, i.e. any trajectory eventually converges to one of equilibrium states. These stability properties are preserved under introduction of any synaptic transmission delay. In addition monotone sensitivity is discussed for weakly coupled cooperative networks and type K monotone networks.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E72-E No.7 pp.863-867
- Publication Date
- 1989/07/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Bio-Cybernetics
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Kiichi URAHAMA, "Global Stability of Some Classes of Neural Networks" in IEICE TRANSACTIONS on transactions,
vol. E72-E, no. 7, pp. 863-867, July 1989, doi: .
Abstract: Global stability of equilibrium states is investigated for a continuous-time model of neural networks and a discrete-time one. Three classes of globally stable networks are introduced. One class called weakly coupled networks is shown to be globally asymptotically stable, i.e. every trajectory eventually converges to a unique equilibrium point. The other two classes of which one is called gradient networks and the other is called type K monotone networks are guaranteed to be completely stable, i.e. any trajectory eventually converges to one of equilibrium states. These stability properties are preserved under introduction of any synaptic transmission delay. In addition monotone sensitivity is discussed for weakly coupled cooperative networks and type K monotone networks.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e72-e_7_863/_p
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@ARTICLE{e72-e_7_863,
author={Kiichi URAHAMA, },
journal={IEICE TRANSACTIONS on transactions},
title={Global Stability of Some Classes of Neural Networks},
year={1989},
volume={E72-E},
number={7},
pages={863-867},
abstract={Global stability of equilibrium states is investigated for a continuous-time model of neural networks and a discrete-time one. Three classes of globally stable networks are introduced. One class called weakly coupled networks is shown to be globally asymptotically stable, i.e. every trajectory eventually converges to a unique equilibrium point. The other two classes of which one is called gradient networks and the other is called type K monotone networks are guaranteed to be completely stable, i.e. any trajectory eventually converges to one of equilibrium states. These stability properties are preserved under introduction of any synaptic transmission delay. In addition monotone sensitivity is discussed for weakly coupled cooperative networks and type K monotone networks.},
keywords={},
doi={},
ISSN={},
month={July},}
Copy
TY - JOUR
TI - Global Stability of Some Classes of Neural Networks
T2 - IEICE TRANSACTIONS on transactions
SP - 863
EP - 867
AU - Kiichi URAHAMA
PY - 1989
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E72-E
IS - 7
JA - IEICE TRANSACTIONS on transactions
Y1 - July 1989
AB - Global stability of equilibrium states is investigated for a continuous-time model of neural networks and a discrete-time one. Three classes of globally stable networks are introduced. One class called weakly coupled networks is shown to be globally asymptotically stable, i.e. every trajectory eventually converges to a unique equilibrium point. The other two classes of which one is called gradient networks and the other is called type K monotone networks are guaranteed to be completely stable, i.e. any trajectory eventually converges to one of equilibrium states. These stability properties are preserved under introduction of any synaptic transmission delay. In addition monotone sensitivity is discussed for weakly coupled cooperative networks and type K monotone networks.
ER -
English
