Based on conditional Lyapunov exponent, the impulsive synchronization form and interval of chaotic systems are studied, which breaks the traditional basic assumptions.

The essence of the gray prediction model is to fit the known data sequence with an exponent form to a curve, and then extend the curve to the future in order to predict the unknown data.

It is proved that the degree distribution of the network obeys power-law form with the exponent-3, and the mean connected degree is given value.