Discrete Memristive Hopfield Neural Network with Grid-Polyhedral Hyperchaos for FPGA-Based Pseudorandom Number Generator.

Abstract

This paper proposes a discrete two-memristor-based Hopfield neural network (DTM-HNN) by integrating two memristors with internal piecewise-linear state functions into a two-neuron Hopfield neural network regarded as a seed map. The DTM-HNN is capable of generating grid-polyhedral hyperchaotic attractors and homogeneous coexisting hyperchaotic attractors, with the structure and scale flexibly regulated by the memristor parameters and scaling factor. Fixed-point and Jacobian analyses show that the fixed points of the seed map are mirrored and scaled by two memristors, enabling tunable attractor positions and amplitudes. Numerical simulations reveal rich dynamic behaviors, including transitions between grid distribution and homogeneous coexistence, which are quantitatively characterized using diagonal distance and spectral entropy. An efficient digital hardware device is developed, supporting online parameter configuration and real-time attractor observation. Furthermore, a spatial-distribution-based hardware pseudorandom number generator (PRNG) is designed, leveraging dynamic switching between grid and coexistence states. The hardware PRNG achieves high throughput and passes all NIST randomness tests, with strong key sensitivity and low resource utilization, demonstrating its practical value in security applications.