Dynamics analysis and DSP implementation of a new four-dimensional discrete memristor hyperchaotic map

Abstract

In recent years, discrete memristors have garnered significant interest from the scientific community due to their nonlinear and adaptive properties. These characteristics make them ideal for use as nonlinear elements in generating chaotic oscillations. However, the current research on the discrete memristor chaotic map is still focused on constructing it by coupling first-order discrete memristors, and the research on coupling higher-order discrete memristors is relatively limited. This paper presents a novel four-dimensional discrete memristor hyperchaotic map that is coupled with a second-order discrete memristor. Through numerical simulations, we analyze the bifurcation diagram and Lyapunov index diagram of the new map with the change of coupling coefficient and various control parameters. Our findings indicate that the map exists in a hyperchaotic state and demonstrates the coexistence of multiple attractors under varying initial conditions. This results in a rich tapestry of dynamic behaviors and high complexity. Moreover, we have implemented the memristor chaotic map by DSP platform.