Hybrid projective synchronization of a class of new chaotic systems

A class of new four-dimensional autonomous chaotic systems are presented, which have wide chaotic or hy-perchaotic parameter range obtained from Lyapunov exponent spectrum, Lyapunov dimension and phase portrait. Based on Lyapunov stability theory and Barbalat's Lemma, adaptive feedback control laws for hybrid projective synchronization (HPS) of the systems are proposed, especially, the controller with the law can be simplified into a single scalar one to achieve complete synchronization. Furthermore, HPS between every two of them with unknown parameters is investigated and adaptive parameter update laws are also developed. Finally, numerical simulations are demonstrated to verify the effectiveness of the strategies.