Design and Performance Analysis of Discrete Memristive Hyperchaotic Systems With Stuffed Cube Attractors and Ultraboosting Behaviors

Memristors are widely used for studying chaotic oscillations due to their special nonlinearity and plasticity. This article presents a framework for constructing the ultraboosting memristive hyperchaotic map. The complexity of the original map can be significantly enhanced by it. It can also effectively resolve the discontinuous chaotic range and low Lyapunov exponent problems of common hyperchaotic systems. There are four hyperchaotic maps that are derived from this framework with ultraboosting behaviors, and they generate cube attractors. Hardware devices based on microcontrollers are built to implement these maps, and the experimental results are highly consistent with the numerical simulations. A pseudorandom number generator is designed using these hyperchaotic maps, and the National Institute of Standards and Technology test results show that the generated pseudorandom numbers have extremely high randomness. Finally, we apply them in developing the image encryption algorithm.