Dynamical analysis on the multistability of high-order neural networks

Authors:
Lili Wang
Affiliations:
Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, PR China
Venue:
Neurocomputing
Year:
2013

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Abstract

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^#^N^"^2 equilibrium points, 2^#^N^"^2 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.