Dynamical analysis on the multistability of high-order neural networks

In this paper, we are concerned with a class of high-order neural networks (HONNs). Rigorous analysis shows that the state components exhibit different dynamical behaviors with respect to external inputs lying in different ranges. And by dividing the index set {1,2, . . . ,n} into four subsets N-J, j= 1,2,3,4, according to different external input ranges, we can conclude that the HONNs have exact 3(#N2) equilibrium points, 2(#N2) of them are locally stable and others are unstable, here #N-2 represents the number of elements in the subset N-2. The results obtained improve and extend some related works. A numerical example is presented to illustrate the effectiveness of our criteria. (C) 2013 Elsevier B.V. All rights reserved.