Controlled chaotic systems for secure communications: FPGA synchronization and control

To enhance secure communication efficiency, this paper proposes a novel four-dimensional single-scroll conservative chaotic system based on the Hamiltonian energy conservation theorem. A multivariate nonlinear active controller and synchronization controller are designed, with dynamic analysis revealing rich chaotic behaviors including multiple chaotic attractor-like structures, attractor-like coexistence, amplitude-modulated chaotic control, and parametric chaos. By extending equilibrium points via a segmentation function, we construct a multi-vortex system with adjustable vortex characteristics in both single and dual directions, achieving high Sample entropy. An active controller ensures state variable convergence to desired values, while a synchronization controller enables precise main system synchronization. Numerical simulations demonstrate flexible synchronization time adjustment through clock frequency tuning, outperforming software-based methods. This work advances chaotic synchronization theory and provides digital circuit solutions for secure communication.