Dynamic properties of neural network with adapting synapses

It is pointed out that two kinds of dynamic processes take place in neural networks. One is the change of activity of each neuron; the other is the change of connection between neurons. When a neural network is learning or developing, both of these two processes take place and interact with each other. The abstracted biological properties of neuron activation and connection modification are used. The learning rule is the Hebbian rule: the connection between two neurons is positively correlated to the correlation of their activities in a long learning time scale. An energy analysis is provided for this network model including both dynamic processes. Some interesting learning features appear. The kind of dynamical system considered here has the unique feature of learning the correlation of input vectors under certain conditions and selecting the final learning results under other conditions