Bursting synchronization of Hind–Rose system based on a single controller

Bursting synchronization of Hind–Rose system is investigated. Two schemes with only a single controller are proposed to synchronize Hind–Rose chaotic system via the back-stepping method. Especially in the second scheme, only one state variable is contained in the controller. Based on Lyapunov stability theory, the sufficient conditions for synchronization are obtained analytically in both cases. Finally, numerical simulations are provided to show the effectiveness of the developed methods.