Design and hardware implementation of 4D memristive hyperchaotic map with rich initial-relied and parameter-relied dynamics

Since the concept of memristor was proposed, the construction of memristive hyperchaotic map has attracted wide attention. In this paper, a new 4D memristive hyperchaotic map is presented, investigating its characteristics such as multi$-$scroll attractors, coexisting attractors, offset boosting, and amplitude modulation. Regulated by variations in parameters, it exhibits extensive and continuous ranges of hyperchaotic behavior, overcoming the discontinuity issue in the chaotic range of traditional maps. Simulation results and numerical analyses demonstrate that it can generate diverse dynamic behaviors and possess superior chaotic properties. The National Institute of Standards and Technology (NIST) test reveals that the generated sequences display a high degree of randomness. A digital hardware platform based on microcomputer is established to verify the physical feasibility. Lastly, its successful application in the development of image encryption algorithm underscores the immense potential in the field of information security.