High-accuracy implementation of biological neural networks (NN) is a task with high computational overheads, especially in the case of large-scale realizations of neuromorphic algorithms. This paper presents a set of piecewise linear FitzHugh–Nagumo (FHN) models, which can reproduce different behaviors, similar to the biological neuron. This paper presents a set of equations as a model to describe the mechanisms of a single neuron, which are implementable on digital platforms. Simulation results show that the model can reproduce different behaviors of the neuron. The proposed models are investigated, in terms of digital implementation feasibility and computational overhead, targeting low-cost hardware realization. Hardware synthesis and physical implementations on FPGA show that the proposed models can produce a range of neuron behaviors with higher performance and lower implementation costs compared to the original model.