npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041


Research Paper

New Physics: Sae Mulli 2017; 67: 357-365

Published online March 31, 2017

Copyright © New Physics: Sae Mulli.

Dynamics Properties of Learning Equations in a Neural Network

Myoung Won CHO*

Department of Global Medical Science, Sungshin Women's University, Seoul 01133, Korea


Received: August 2, 2016; Revised: November 7, 2016; Accepted: November 11, 2016

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.


The firing dynamics and the learning dynamics in a neural network depend on each other, but they can be represented by independent equations in virtue of their different pace. In comparison with that, the firing dynamics is much studied as an important issue in the field of nonlinear dynamics, but the dynamic properties of the learning equations are still not well understood. A learning equation represented by a matrix differential equation can possess peculiar dynamic properties in addition to the dynamic properties of a general dynamics equation represented by a vector differential equation. In this paper, based on studies of the presented learning models, we introduce systematically the dynamics properties of the learning equations, and we discuss theoretical methods to represent and analyze effectively the dynamics in a huge neural network, like the brain.

Keywords: Neural network, Learning dynamics