Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales
Abstract
The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points.
Cite
Text
Meyer-Bäse et al. "Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales." Neural Computation, 1996. doi:10.1162/NECO.1996.8.8.1731Markdown
[Meyer-Bäse et al. "Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales." Neural Computation, 1996.](https://mlanthology.org/neco/1996/meyerbase1996neco-singular/) doi:10.1162/NECO.1996.8.8.1731BibTeX
@article{meyerbase1996neco-singular,
title = {{Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales}},
author = {Meyer-Bäse, Anke and Ohl, Frank W. and Scheich, Henning},
journal = {Neural Computation},
year = {1996},
pages = {1731-1742},
doi = {10.1162/NECO.1996.8.8.1731},
volume = {8},
url = {https://mlanthology.org/neco/1996/meyerbase1996neco-singular/}
}