Generalized Projective Synchronization of Fractional-order Hyperchaotic Lu and Hyperchaotic Cai System via Active Control

This paper studies the design of feedback controllers to achieve generalized projective synchronization (GPS) between two fractional derivative order hyperchaotic Lu systems (similar), and between hyperchaotic Cai system and fractional-order hyperchaotic Lu system (dissimilar). First, new sliding surface is defined for GPS of fractional-order Lu-Lu and Lu-Cai systems. Then the results of the GPS achieved in this article is proved using Lyapunov stability theorem. Without using Lyapunov exponents, the active feedback control method to achieve GPS of fractional-order hyperchaotic Lu-Lu and Cai-Lu is calculated. Performance of the proposed method is shown, using numerical simulations.