Synchronization between the spatial Julia sets of complex Lorenz system and complex Henon map

In this paper, the definition of Julia set of complex Lorenz system is introduced. By using two different nonlinear coupling methods, the different structure synchronization between the Julia sets of complex Lorenz system and Henon map is investigated. In the former method, the synchronization is realized by adjusting a single coupling parameter. In order to quantify the synchronization process with the changing coupling parameter, a mathematical approach is proposed. The later method constructs a novel coupling term by replacing the coupling parameter with a coupling matrix. Through choosing a proper coupling matrix, the synchronization is also achieved. Numerical simulations verify the effectiveness of the methods.