Discrete Memristor-Based Hyperchaotic Map and Its Analog Circuit Implementation

In this paper, control parameters are incorporated into the absolute discrete memristor (A-DM) map proposed by Bao, and its dynamic characteristics are analyzed. Subsequently, the A-DM is introduced into the traditional sine map via parallel coupling to construct a new sine A-DM hyperchaotic map (SAHM). The dynamics of SAHM are investigated using Lyapunov exponent spectra and bifurcation diagrams, with additional analysis on its multi-stability and symmetry properties. Circuit simulations successfully realize the attractors corresponding to SAHM under typical parameters. Evaluations of SAHM’s complexity, performance comparisons, and its application to pseudorandom number generators (PRNG) demonstrate that SAHM is well-suited for secure encryption scenarios.