Necessary and sufficient condition for multistability of neural networks evolving on a closed hypercube

被引：29

作者：

Di Marco, Mauro ^{[1
]}

Forti, Mauro ^{[1
]}

Grazzini, Massimo ^{[1
]}

Pancioni, Luca ^{[1
]}

机构：

[1] Univ Siena, Dept Informat Engn & Math Sci, I-53100 Siena, Italy

来源：

NEURAL NETWORKS | 2014年 / 54卷

关键词：

Neural networks; Multistability; Differential variational inequalities; Cooperative dynamical systems; Nonsmooth dynamical systems; COMPLETE STABILITY; ACTIVATION DYNAMICS; EQUILIBRIUM POINTS; LINEAR-SYSTEMS; CONVERGENCE;

D O I：

10.1016/j.neunet.2014.02.010

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The paper considers nonsmooth neural networks described by a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs include the relevant class of neural networks, introduced by Li, Michel and Porod, described by linear systems evolving in a closed hypercube of R-n. The main result in the taper is a necessary and sufficient condition for multistability of DVIs with nonsymmetric and cooperative (nonnegative) interconnections between neurons. The condition is easily checkable and provides a sharp bound between DVIs that can store multiple patterns, as asymptotically stable equilibria, and those for which this is not possible. Numerical examples and simulations are presented to confirm and illustrate the theoretic findings. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：38 / 48

页数：11

共 51 条

[1]

Amari Shin-Ichi., 1982, COMPETITION COOPERAT

[2] Multi-stability in monotone input/output systems [J].