Designing a Novel Memristor-based Chaotic System Pumped by Cosine and its Application in Image Encryption

Memristor, a nonlinear element with nanometer size, can be applied in chaotic system and thus enhancing complexity of the chaotic system. Therefore, a novel memristor-based 4D multi-scroll chaotic system via cosine is successfully designed in this letter. The main feature of this system is that the scroll number are sensitive to initial values, the transient simulation time, the flux variation of memristor and the strength of memristor, which is a significant difference from other chaotic systems reported before. Furthermore, the chaotic characteristics have been declared by using time series, 0-1 test chart, and Poincare maps. Besides, the number of scrolls can be controlled by designing a state feedback controller to select the ideal number of scrolls, and such a method for controlling the scroll number is extremely meaningful in suppressing the nonlinearity of chaotic systems. Finally, an algorithm for image encryption is proposed based on the bitwise and cross-transition between adjacent pixels. Both confusion and diffusion are related to the memristor-based chaotic system. Many statistical tests and security analysis show that this algorithm has a good security performance, which can be compared with other recently proposed image encryption algorithms.