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}{1,2,…,n} into four subsets Nj,j=1,2,3,4, according to different external input ranges, we can conclude that the HONNs have exact 3#N23#N2 equilibrium points, 2#N22#N2 of them are locally stable and others are unstable, here #N2#N2 represents the number of elements in the subset N2N2. The results obtained improve and extend some related works. A numerical example is presented to illustrate the effectiveness of our criteria.