New identification and control methods of sine-function Julia sets

In this paper, we propose two new methods to realize drive-response system synchronization control and parameter identification for two kinds of sine-function Julia sets. By means of these two methods, the zero asymptotic sliding variables and the stability theory in difference equations are applied to control the fractal identification. Furthermore, the problem of synchronization control is solved in the case of a drive system with unknown parameters, where the unknown parameters of the drive system can be identified in the asymptotic synchronization process. The results of simulation examples demonstrate the effectiveness of the new methods.