A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper. With this method, the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved. Control and synchronization of generalized Julia sets are also achieved with this optimal control method. The simulations illustrate the efficacy of this method.
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.
