Dynamics and circuit implementation of a novel coupled discrete memristive system

This paper presents the design and analysis of a 3D memristor-based discrete chaotic system, combining theoretical exploration with practical implementation. The proposed system is derived from a sine discrete memristor model and exhibits rich hyperchaotic dynamics, as demonstrated through stability analysis, bifurcation diagrams, Lyapunov exponents, and complexity measures (spectral entropy $SE$ and $C_0$ complexity). Numerical simulations reveal broad chaotic regions and extreme sensitivity to parameter variations, including hyperchaos with multiple positive Lyapunov exponents. A digital and analog realization is achieved via a PSim-simulated circuit employing sample-and-hold modules, operational amplifiers, and nonlinear components, with results closely matching numerical predictions. Furthermore, the system is leveraged to construct a pseudo-random number generator (PRNG), which successfully passes all NIST SP800-22 randomness tests, validating its potential for secure communication and encryption applications. The study bridges theoretical chaos analysis with tangible electronic implementation, offering insights into memristive discrete systems for high-performance chaos-based technologies.