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