A Characterization of Stability of Discrete Hopfield Neural Networks
Wei Ye, Zongben Xu, Cao Huai-xin, Jianhua Zhang · Project Euclid (Cornell University) · 2003
We discuss the stability of discrete Hopfield neural networks (Shortly, DHNNs) in synchronous mode. To do this, we introduce an equivalent relation in the set $M_{m,\mathfrak{n}}(R)$ of all $m$ by $n$ matrices over the real field $R$ and then obtain a classification of matrices. Thanks to this classification we establish a classification of all discrete Hopfield neural networks with $n$ neurons in such a way that two DHNNs belong to the same class if and only if they have the same dynamic property. Lastly, a characterization of the stability of a DHNN with two neurons in synchronous mode is obtained.