Chaos control and hybrid projective synchronization of several new chaotic systems

Abstract

The problems on purposefully creating and controlling chaos are investigated. First, several new 4D chaotic systems are presented based on a 3D chaotic system and three dynamical characteristics are verified. Second, it is demonstrated that they can be stabilized to their equilibrium points by a same single scalar adaptive feedback control law. Third, two of the chaotic systems with constant parameters are in hybrid projective synchronization (HPS) by presented adaptive feedback control strategies, which can be simplified into a scalar form for identical drive–response systems to achieve complete synchronization. Furthermore, HPS between two of the chaotic systems with response system parameters unknown is also considered and adaptive parameter update laws are developed. Numerical simulations show their characteristics and verify the effectiveness of the strategies.