Multistability of neural networks with a class of activation functions

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≥) 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. © 2009 Springer Berlin Heidelberg.