Combination Projective Synchronization in Fractional-Order Chaotic System with Disturbance and Uncertainty

Abstract

In this manuscript, we study combination projective synchronization (CPS). In CPS, matrix projective combination synchronization (MPCS) and inverse matrix projective combination synchronization (IMPCS) between non-identical fractional-order complex chaotic systems subjected to uncertainty and external disturbance is investigated. Matrix projective synchronization (MPS) and inverse matrix projective synchronization is obtained when the scaling factor is a constant matrix, which gives the assurance of high security in secure communication and image encryption. Based on the Lyapunov stability theory and appropriate active control technique, the MPCS and IMPCS between two master systems and one slave system has been achieved. Based on the MPCS synchronization, a scheme of secure communication is presented, and the message signals are transmitted using the chaotic signal masking method. Finally, numerical simulations have been provided, which shows that our theoretical results are in complete agreement will the graphical one.