A modular-bias-sin chaotification method for enhanced discrete memristor chaotic maps

This paper proposes a novel modular-bias-sin chaotification method (MBSC) to address the limitations of existing discrete memristor (DM)-based chaotic maps. By applying MBSC to several fundamental discrete memristors, the enhanced chaotic variants are constructed. Comprehensive dynamical analyses, including attractor phase diagrams, Lyapunov exponents, bifurcation diagrams, Shannon entropy (SE) complexity, and chaotic region scale (CRS), demonstrate that the MBSC-enhanced maps outperform the original DM maps and existing modified models. Specifically, they exhibit wider chaotic parameter ranges, larger Lyapunov exponents, higher SE complexity, and robust hyperchaotic behavior. To validate practical applicability, a pseudo-random number generator (PRNG) based on the enhanced chaotic maps is implemented, which passes all NIST SP 800-22 statistical tests, confirming its high randomness and suitability for security-sensitive applications.