A Microcontroller Implementation of a Pseudo-random Bit Generator based on a 2D Discrete Memristive Hyperchaotic Map

Discovered by Chua in 1971, the memristor has established itself as the fourth essential electrical element, in addition to resistor, capacitor, and inductor. With the formalization of discrete memristors, numerous models have been developed. Currently, there is a growing interest in exploring the complex dynamical behaviors that manifest when memristors are integrated into discrete chaotic maps, driven by the practical applications of these systems. In this study, a Cubic map model that incorporates a discrete memristive function is introduced and implemented via a microcontroller for the purpose of realizing a chaotic pseudo-random bit generator. To investigate the dynamic characteristics of the system, a variety of nonlinear tools are employed, including bifurcation diagrams, maximal Lyapunov exponent diagrams, and phase portraits. Significant phenomena associated with chaos were identified, encompassing periodic, chaotic and hyperchaotic attractors, and the emergence of chaos through mechanism of period doubling phenomena and quasiperiodic behavior.