Recent memristive neuron models have improved the ability of researchers to describe the operation of biological neurons. We employ FPGA implementation for a memristive neuron model, FPGA implementation provides an improved hardware system for mimicking brain behavior, and provides a better understanding of neurological phenomena. In this manuscript, a memristive Hindmarsh–Rose neuron model taking into account the influence of electromagnetic radiation and two multiplierless approximations of this model are presented. These approximations are piecewise linear (PWL) model and hybrid model, which mimic the behaviors of the original model. In the hybrid model, power 2-based approximation and a novel approximation are used simultaneously. The proposed models were subjected to error analysis, revealing that the PWL model exhibited mean NRMSEs of 3.56% and 2.3% for bursting and spiking modes, respectively. On the other hand, the hybrid model displayed mean NRMSEs of 1.92% and 1.34% for bursting and spiking modes. According to the FPGA implementation results, the PWL model yields the overall resources saving of 75.82% and 47.8% speed-up. But in the hybrid model, by optimizing the approximation functions, in addition to obtaining higher accuracy, better results are provided with a 67.3% improvement in the maximum frequency and the 78.64% saving in hardware resources.
