Nonlinear Dynamics and Symbolic Dynamics of Neural Networks
Abstract
A piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks. A symbolic representation of the dynamics in this equation is given as a directed graph on an N-dimensional hypercube. This provides a formal link with discrete neural networks such as the original Hopfield models. Analytic criteria are given to establish steady states and limit cycle oscillations independent of network dimension. Model networks that display multiple stable limit cycles and chaotic dynamics are discussed. The results show that such equations are a useful and efficient method of investigating the behavior of neural networks.
Cite
Text
Lewis and Glass. "Nonlinear Dynamics and Symbolic Dynamics of Neural Networks." Neural Computation, 1992. doi:10.1162/NECO.1992.4.5.621Markdown
[Lewis and Glass. "Nonlinear Dynamics and Symbolic Dynamics of Neural Networks." Neural Computation, 1992.](https://mlanthology.org/neco/1992/lewis1992neco-nonlinear/) doi:10.1162/NECO.1992.4.5.621BibTeX
@article{lewis1992neco-nonlinear,
title = {{Nonlinear Dynamics and Symbolic Dynamics of Neural Networks}},
author = {Lewis, John E. and Glass, Leon},
journal = {Neural Computation},
year = {1992},
pages = {621-642},
doi = {10.1162/NECO.1992.4.5.621},
volume = {4},
url = {https://mlanthology.org/neco/1992/lewis1992neco-nonlinear/}
}