Active controller design for the GPS of four-wing chaotic systems

Abstract

Generalized projective synchronization (GPS) of chaotic systems is a new type of synchronization, which is a general form of synchronization compared to other types of synchronization such as complete synchronization (CS), antisynchronization (AS), hybrid synchronization (HS), projective synchronization (PS), etc. There are many types of techniques available for synchronizing chaotic systems such as delayed feedback control, sampled-data feedback control, sliding mode control, backstepping control, etc. In this paper, we have used active control method for GPS of four-wing chaotic systems, viz. Wang four-wing chaotic system (2009) and Liu four-wing chaotic system (2009). Explicitly, we derive active controllers for GPS of identical Wang four-wing chaotic systems, identical Liu fourwing chaotic systems and non-identical Wang and Liu four-wing chaotic systems. Main GPS results in this work have been proved with the help of Lyapunov stability theory. MATLAB plots are shown to demonstrate the GPS results for Wang and Liu fourwing chaotic systems.