This paper presents a numerical analysis of the role of asymptotic dynamics in the design of hardware-based implementations of the generalised integrate-and-fire (gIF) neuron models. These proposed implementations are based on extensions of the discrete-time spiking neuron model, which was introduced by Soula et al., and have been implemented on Field Programmable Gate Array (FPGA) devices using fixed-point arithmetic. Mathematical studies conducted by Cessac have evidenced the existence of three main regimes (neural death, periodic and chaotic regimes) in the activity of such neuron models. These activity regimes are characterised in hardware by considering a precision analysis in the design of an architecture for an FPGA-based implementation. The proposed approach, although based on gIF neuron models and FPGA hardware, can be extended to more complex neuron models as well as to different in silico implementations.