Dynamics Analysis and Projective Synchronization of a Novel Fractional-Order System and Application in Image Encryption

Fractional-order system attracted researcher's attention due to the complicated behaviors and memory properties. To further investigate the dynamics of a fractional-order system and its application, a fractional-order system with a memristor is constructed based on the Sprott E system. The dynamics of the addressed system is studied, and projective synchronization is realized by designing controllers. Numerical simulations verify the theoretical results. Furthermore, according to the projective synchronization of the proposed systems, an image encryption algorithm is put forward and its effectiveness is analyzed from various aspects. By contrast with scrambling diffusion encryption algorithm, the addressed encryption algorithm shows certain advantages, because it makes full use of the characteristics of projective synchronization of chaos systems and can resist exhaustive attacks effectively.