Discrete memristive hyperchaotic map with heterogeneous and homogeneous multistability and its applications

Memristors, due to their inherent nonlinear characteristics, are widely applied in discrete dynamical systems. However, existing research on the construction of discrete memristors is limited, and their applications in discrete dynamical systems remain confined. To address this gap, this paper introduces four novel discrete memristor models, selecting one that combines an exponential function with a sine function. By coupling this model with a two-dimensional sine map, we construct a three-dimensional discrete memristor-based hyper- chaotic map (SEDMM) that exhibits greater complexity and a broader chaotic region. Analysis reveals that the map displays a variety of dynamical behaviors, including periodic, quasiperiodic, multi-periodic, chaotic, and hyperchaotic states. More importantly, it shows both heterogeneous and homogeneous multistability. Furthermore, a novel color image encryption scheme is developed, and experimental results confirm its improved unpredictability. Finally, the hyperchaotic attractor is captured using a Digital Signal Processor (DSP), and experimental validation confirms the scientific validity and feasibility of the proposed map.