Two-Dimensional Discrete Bi-Neuron Hopfield Neural Network With Polyhedral Hyperchaos

Designing low-dimensional chaotic maps with strong resistance to chaos degradation is of great significance to chaos theory and chaos-based applications. The famous Hopfield neural network (HNN) is an artificial neural network, which has been widely studied and applied. However, discrete HNNs, especially their complex dynamics and hyperchaotic attractors with complex structures, are rarely reported in the literature. To this end, this paper proposes a two-dimensional discrete model of bi-neuron HNN with sine activation functions. The fixed points with stability analysis are theoretically explored and complex dynamics with coexisting behaviors are numerically revealed. The discrete model has infinitely many fixed points and emerges various polyhedral chaotic/hyperchaotic attractors with marvelous fractal structures. Besides, using the model, we design four pseudorandom number generators (PRNGs) and test their randomness by TestU01 suite. The results manifest that the PRNGs have high randomness and strong resistance to chaos degradation. Lastly, an FPGA hardware platform is developed to implement the proposed discrete model, upon which the polyhedral chaotic/hyperchaotic attractors are experimentally acquired to validate the numerical results, and two hardware PRNGs are fabricated to provide the true pseudorandom numbers (PRNs).