Design and analysis of a 2D discrete memristive map

Abstract This study proposes a novel 2D memristive hyperchaotic map (2DMHM) with hyperbolic tangent and absolute value functions. The 2DMHM exhibits an infinite of fixed points in a set of lines on the y -axis, with stability characteristics partitioned across memristor parameters and initial condition planes. System dynamics are systematically investigated through bifurcation analysis, Lyapunov exponent spectra, and basin of attraction, trajectory plots, revealing remarkable multistability and initial-sensitive chaotic behavior. The map demonstrates superior spectral entropy (SE) complexity across critical parameter ranges, significantly outperforming conventional chaotic systems. A microcontroller-based digital implementation validates the physical realizability of 2DMHM, while the NIST test success rate demonstrates its exceptional performance in pseudorandom number generation. These results establish 2DMHM as a promising candidate for secure communication systems and cryptographic applications.