Name
Abstract | ||
|---|---|---|
In this paper, we investigate the multistability of neural networks with a class of activation functions, which are nondecreasing piecewise linear with 2r (r *** 1) corner points. It shows that the n -neuron neural networks can have and only have (2r + 1) n equilibria under some conditions, (r + 1) n of which are locally exponentially stable and others are unstable. In addition, we discuss the attraction basins of the stable equilibria for the two-dimensional case and found out that under several conditions, the stable manifolds of the unstable equilibria precisely comprise of the bounds of each attractor. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/978-3-642-01507-6_38 | ISNN (1) |
Keywords | Field | DocType |
corner point,unstable equilibrium,stable equilibrium,neural networks,activation functions,neural network,activation function,attraction basin,stable manifold,two-dimensional case,n equilibrium,neuron neural network,piecewise linear | Attractor,Stable manifold,Recurrent neural network,Exponential stability,Artificial intelligence,Multistability,Piecewise linear function,Manifold,Discrete mathematics,Pattern recognition,Activation function,Pure mathematics,Mathematics | Conference |
Volume | ISSN | Citations |
5551 | 0302-9743 | 2 |
PageRank | References | Authors |
0.45 | 10 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lili Wang | 1 | 269 | 13.90 |
| Wenlian Lu | 2 | 1331 | 93.47 |
| Tianping Chen | 3 | 3095 | 250.77 |