A controlling method for realizing chaotic synchronization and generating a special multi-wing attractor

The complete synchronization and anti-synchronization(C-A synchronization) can be achieved when chaotic system has some degree of symmetry. In this paper, C-A synchronization is improved based on the linear separation method to achieve the C-A projective synchronization, that is, the drive and response vectors synchronize up to the scaling factor in the Lorenz system. Furthermore, the controller obtained by the improved C-A synchronization is modified by a large quantity of trial-and-error computer simulations to generate a special multi-wing chaotic attractor. By the theoretical analysis and numerical simulations, some basic dynamical properties of the controlled Lorenz system are investigated. Research results show that this system has complex and interesting chaotic and hyperchaotic dynamics.