Name
Title | ||
|---|---|---|
Necessary and sufficient condition for multistability of neural networks evolving on a closed hypercube. |
Abstract | ||
|---|---|---|
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 Rn. The main result in the paper 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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.neunet.2014.02.010 | Neural Networks |
Keywords | Field | DocType |
Neural networks,Multistability,Differential variational inequalities,Cooperative dynamical systems,Nonsmooth dynamical systems | Differential inclusion,Mathematical optimization,Linear system,Multistability,Artificial neural network,Hypercube,Mathematics,Variational inequality,Stability theory | Journal |
Volume | Issue | ISSN |
54 | 1 | 0893-6080 |
Citations | PageRank | References |
5 | 0.45 | 27 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mauro Di Marco | 1 | 205 | 18.38 |
| Mauro Forti | 2 | 398 | 36.80 |
| Massimo Grazzini | 3 | 131 | 11.01 |
| Luca Pancioni | 4 | 207 | 17.58 |