Sine-Transform-Based Dual-Memristor Hyperchaotic Map and Analog Circuit Implementation

Memristor, as a fundamental circuit element with strong nonlinearities, particularly a periodic memristor, plays a key role in constructing discrete maps with significant chaotic complexity. However, the initial boosting of extreme multistability remains insufficiently explored in current studies. To further improve the dynamical behavior and complexity of discrete memristor (DM) maps, a dual-memristor self-feedback and sinusoidal transformation modeling strategy is proposed. Control parameter-related dynamical properties and specifically memristor initial-boosted dynamical performances are further investigated through 1-D/2-D bifurcation diagrams, 1-D/2-D Lyapunov exponents (LEs), and attractor phase diagrams. Numerical results demonstrate that the suggested map not only generates rich dynamics but also exhibits excellent initial-boosted extreme multistability. Furthermore, the performance evaluations are carried out on strange attractors, confirming the enhanced complexity of the hyperchaotic attractor through noteworthy complexity indicators. Then, an analog circuit is developed and implemented to validate the accuracy of the numerical results further. Finally, a novel color multi-image encryption strategy based on enhanced hyperchaotic sequences is proposed, and its security and performance are thoroughly analyzed to prove robustness and reliability, increasing its practical application value.