The generalized Q-S synchronization between the generalized Lorenz canonical form and the Rössler system

In this paper, we investigate the generalized Q-S synchronization between the generalized Lorenz canonical form and the Rössler system. Firstly, we transform an arbitrary generalized Lorenz system to the generalized Lorenz canonical form, and the relation between the parameter of the generalized Lorenz system and the parameter of the generalized Lorenz canonical form are shown. Secondly, we extend the scheme present by [Yan ZY. Chaos 2005;15:023902] to study the generalized Q-S synchronization between the generalized Lorenz canonical form and the Rössler system, the more general controller is obtained. By choosing different parameter in the generalized controller obtained here, without much extra effort, we can get the controller of synchronization between the Chen system and the Rössler system, the Lü system and the Rössler system, the classic Lorenz system and the Rössler system, the Hyperbolic Lorenz system and the Rössler system, respectively. Finally, numerical simulations are used to perform such synchronization and verify the effectiveness of the controller.