A highly chaotic fractional-order system with a four-wing attractor and its synchronization

In this paper, a new four-wing attractor is reported in a fractional-order chaotic system. The chaoticness of the proposed system is investigated by obtaining Lyapunov exponents and compared with that of well-known chaotic systems in the literature. The findings reveal extremely high chaoticness of the introduced system which makes it a proper choice for encryption systems and secure communication. Furthermore, synchronization of the proposed system is studied in this paper. Sliding mode control has been used for this purpose and it is proven and illustrated that the synchronization error is asymptotically stable by employing the Lyapunov stability theorem.