Compact Landau–Khalatnikov FeFET polarization model and its 5D hyperchaotic integration with multi-scroll attractors

The demand for high-dimensional and complex chaotic systems for secure communication and cryptography applications has motivated the development of novel hardware-based oscillators. This paper presents a novel five-dimensional (5D) chaotic system developed by integrating a compact, physics-based Ferroelectric Field-Effect Transistor (FeFET) polarization model within a Lorenz-type core. The proposed FeFET model, which is based on the Landau–Khalatnikov (LK) equation, is first presented and comprehensively tested. It captures the important hysteretic polarization dynamics that give it both nonlinearity and memory. A comprehensive analysis, including phase portraits, equilibrium point stability, and Lyapunov exponents, shows that the resulting 5D system is chaotic. In addition, a Parallel Fractal Algorithm (PFA) is used to systematically generate multi-scroll attractors through one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) folding. The results demonstrate that this PFA-driven topological folding not only scales the attractor complexity up to 256 distinct scrolls but also induces a dynamic transition from simple chaos to hyperchaos driven by high topological complexity. To validate practical feasibility, the proposed system is experimentally implemented using an STM32 microcontroller. Furthermore, its cryptographic robustness is demonstrated through a 3D biomedical volume encryption application. These results confirm that the proposed system is a promising option for use in image encryption and secure communication systems.