An attractor-controllable memristive Hopfield neural network and its application on voice encryption

Due to the unpredictability, sensitivity, and complexity of chaotic sequences, they have become special tools in various security applications. Previous studies have primarily focused on general multi-scroll attractor chaotic systems, while research on symmetric attractor-controllable multi-scroll chaotic systems remains relatively limited. Symmetric attractor-controllable multi-scroll chaotic systems typically exhibit more flexible and diverse evolutionary characteristics and higher stability, potentially leading to more stable system responses. Therefore, an attractor-controllable memristive Hopfield neural network (AMHNN) model is proposed in this work. By implementing multilevel logic pulse modulation of memristor synaptic coupling, the proposed AMHNN model enables the controllable generation of symmetric vortex-like double-scroll attractors. Dynamic analysis demonstrates that the AMHNN model can produce 1 to 18 symmetric double-scroll attractors under parameter modulation, with their quantity determined by memristor parameters and pulse stages. When the coupling strength $k_1>0.7$, the system continuously transitions between chaotic and periodic behaviors through bifurcation, and the maximum Lyapunov exponent remains positive, verifying the stability of chaotic characteristics. Hardware implementation based on Xilinx ZYNQ-7000 series FPGA shows that the oscilloscope-measured phase diagrams highly align with the simulation results, confirming the reliability of theoretical analyses. This research provides a solution for chaotic encryption that balances dynamical complexity and engineering feasibility, and its controllable attractor characteristics demonstrate application potential in scenarios such as voice encryption.