Control and synchronization of Julia sets in coupled map lattice

In this paper, we achieve the control and synchronization of Julia sets in coupled map lattice using gradient control and optimal control respectively. The control of the Julia sets is accomplished by controlling the stable space of the fixed plane. Moreover, the synchronization of two different Julia sets is also accomplished by their trajectories synchronization. To verify the feasibility of these control methods, we consider the Julia sets, whose lattice length is two, as examples to achieve their control and synchronization using different methods respectively. The numerical simulations are also shown to illustrate the effectiveness of these control methods.

Research highlights
► The control and synchronization of discrete complex systems—Julia sets in coupled map lattice are studied.
► The gradient and optimal control methods are employed to realize the control and synchronization.
► The mathematical conditions are presented to accomplish the control of Julia sets in coupled map lattice.
► The mathematical conditions are given to achieve the synchronization of two different Julia sets in coupled map lattice.