Received August 2, 2016; Revised November 7, 2016; Accepted November 11, 2016.
The firing dynamics and the learning dynamics in a neural have dependency with 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, the dynamics properties of learning equations is less understood yet. A Learning equation represented by a matrix differential equation can posses peculiar dynamics properties in addition to the dynamics properties of a general dynamics equation represented by a vector differential equation. In this paper, based on the studies in the presented learning models, we introduce systematically the dynamics properties of learning equations. And, we discuss the theoretical methods to represent and analyze effectively the dynamics in a huge neural network, like the brain.