Control of Julia Sets in Generalized Alternated System

In this paper, we first introduce the generalized alternated system. The definition of the Julia set in the generalized alternated system is given, which is called a generalized alternated Julia set. Then, we achieve the control of generalized alternated Julia sets by applying the classic control methods, which are gradient control and optimal control. In addition, the synchronization between two different generalized alternated Julia sets is implemented using gradient control and optimal control. The simulations illustrate the effectiveness and correctness of these two control methods, and the results are displayed in 2D computer graphics.