Xingce Liu, Dongsheng Yang, Yinghua Yang, Ping Yuan, Yating Lin
At present, little research has been done on discrete second-order memristors, while research has focused on discrete first-order memristors. To investigate the memory characteristics of discrete second-order memristors and their influence on chaotic maps, a new discrete second-order memristor is proposed, and its memory characteristics are investigated. Subsequently, a novel four-dimensional hyperchaotic mapping(4D-HM) is obtained by coupling it with the traditional chaotic mapping. Then, the chaotic characteristics of hyperchaotic map is investigated by the Bifurcation diagram, Lyapunov exponents (LEs) and the phase diagram of the 4D-HM. It is worth mentioning that the phenomenon of coexistence of attractors has been discovered in the 4D-HM. This feature makes the 4D-HM more suitable for many chaotic based engineering applications. Therefore, the 4D-HM is applied to the field of image encryption. To demonstrate the security and reliability of the encryption scheme, the simulation results of the scheme are analyzed. Finally, the process of theoretical analysis of the 4D-HM is demonstrated by DSP implementation. Because of its complex dynamical characteristics, the 4D-HM has great potential application value.