A hyperchaotic map with a new discrete memristor model: Design, dynamical analysis, implementation and application

Abstract

The memristor has received much attention in recent years because of its natural nonlinearity, but the research on discrete memristor is just beginning. For this reason, a new discrete memristor model is constructed, and a new three-dimensional hyperchaotic map is constructed by coupling the new discrete memristor. Firstly, the stability of the map is discussed. And then, the dynamical characteristics are analyzed by using the phase diagram, Lyapunov exponent spectrum (LEs), bifurcation diagram and attractor basins, etc. Meanwhile, the state transition and the attractor coexistence with periodic, quasi-periodic, chaotic and hyperchaotic have been studied. In particular, the hyperchaotic map is implemented on the DSP hardware platforms, demonstrating the realizability of the map. Finally, the discrete hyperchaotic map is applied to image encryption. The results of the study provide a reference for the application and teaching of discrete memristor circuits in chaos.