The training process of Kohonen neural network is firstly divided into two phases

the formation phase of self-organizing topology preserve mapping and the post-training phase.Then an investigation is made into the topology preserve property

the neighborhood relationship

the competition and the division of receptive field of the neurons in the post-training phase.Furthermore

the quantitative analysis of probability distribution is given to the one dimensional neural array in the case of arbitrary distribution input

and the iterative formulas of the stated weights of neurons are obtained. Finally

the explicit solution of the static weights is presented to the uniform distributed input.