Hidden extreme multistability in a smooth flux-controlled memristor based four-dimensional chaotic system and its application in image encryption

Abstract

This paper introduces and investigates the dynamic analysis of a four-dimensional chaotic system based on a flux-controlled memristor and its application in image encryption. The analysis of equilibrium points of the system shows that it has no equilibrium points and therefore belongs to the family of systems with hidden attractors. It is demonstrated by computational simulations that the system under study experiences rich and complicated dynamics such as coexisting hidden attractors, hidden extreme multistability, offset boosting dynamics and antimonotonicity. A physical circuit that can reproduce the complex behaviors of the system is constructed and realized. The results are in agreement with those from computational simulations. According to the interesting features of the system, it is exploited to generate random bits for image encryption. The robustness and efficiency of the designed image encryption algorithm are tested by providing some statistical tests and security performances. It is found that the designed image encryption algorithm is efficient and robust compared to other image encryption algorithms investigated in some other recent related works.