Exploring Hybrid FitzHugh-Rinzel (FHR) Neuron Model Behavior: Cost-Effective FPGA Implementation for High-Frequency and High-Precision Matching by Electromagnetic Flux Effects

Effective implementation of spiking neuron models in hardware is crucial for real systems. Utilizing the main capabilities of FPGAs, this paper introduces a highly precise method for evaluating nonlinear functions. The approach relies on effectively matching trigonometric-based functions to approximate the nonlinear terms of a Fitzhugh-Rinzel neuron model uses the electromagnetic flux coupling with a focus on cost-effectiveness and high-speed digital implementation using the CORDIC algorithm and multiplierless design. The close correspondence between the approximate functions and the nonlinear functions of the original model results in minimal errors in the outputs of the proposed model compared to the original model which reduces the lead and lag of signals between the original model and the proposed models. For the digital FPGA implementation of the FHR neuron model, we employed the Virtex-5 board to validate and synthesize the suggested method. In this scenario, the proposed FHR model demonstrates superior performance in terms of speed and cost compared to the original model. The speed-up of our proposed model is about 6 times faster than the original model (414.86 MHz compared to 69.232 MHz) and also, the number of fitted neurons for our proposed approach is about 6.66 times (20 compared to 3).