Discrete Two-Heterogeneous-Neuron HNN and Chaos-Based Hardware Poisson Encoder

Nonlinear activation function is the most essential factor that enables Hopfield neural networks (HNNs) to generate complex dynamics. However, less attention has been paid to the activation function. In this article, we propose a simple discrete model of self-connectionless HNN in which two heterogeneous neurons have different activation functions of sine and hyperbolic tangent. By theoretical and numerical methods, we explore coexisting bifurcation behaviors induced by Neimark-Sacker bifurcations and multifolded hyperchaotic attractors caused by multiple fixed points with different stability. We also evaluate the randomness of these multifolded hyperchaotic sequences and implement the discrete model on field programmable gate array (FPGA) hardware device. In brief, this discrete model with simple algebraic equations has the simplest connection structure under the two-heterogeneous-neuron HNN framework, but it can generate various multifolded hyperchaotic attractors with high randomness. Additionally, based on FPGA hardware device, a chaos-based hardware Poisson encoder is developed to implement the reconstruction of gray image.