Stability and periodicity of discrete Hopfield neural networks with column arbitrary-magnitude-dominant weight matrix

Authors:
Jun Li;Jian Yang;Weigen Wu
Affiliations:
School of Computer Science and Technology, Nanjing University of Science and Technology, 200# Xiao Lin Wei Street, Nanjing 210094, China and College of Computer, Pan Zhi Hua University, 10# Airpor ...;School of Computer Science and Technology, Nanjing University of Science and Technology, 200# Xiao Lin Wei Street, Nanjing 210094, China;College of Computer, Pan Zhi Hua University, 10# Airport Road, Panzhihua 617000, China
Venue:
Neurocomputing
Year:
2012

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Abstract

Stability and periodicity of neural networks is important behavior in biological and cognitive activities. In order to better simulate a biological genuine model, a special kind of discrete Hopfield neural networks (SDHNNs) in which every neuron has only one input is considered. By applying permutation theory and mathematical induction, we prove that the SDHNN always converges to a stable state or a limit cycle. The SDHNN is extended to the discrete Hopfield neural networks with column arbitrary-magnitude-dominant weight matrix (DHNNCAMDWM) in which there only exits a magnitude-dominant element in every column. Some important results, especially the periodic stability of the DHNNCAMDWM, are obtained. And the XOR problem is successfully solved by the results.