5.
This study focuses on the experimental realization of the fractional-order FitzHugh–Nagumo (FHN) neuron model. Firstly, a second-order approximation function is included to the FHN neuron model to satisfy the fractional-order definition. Since these approximation functions can meet the response of the ideal system only in a limited frequency band, the identification of their center frequency is very critical. Thus, the center frequency ‘ωc’ of this second-order approximation functions is swept until getting the spiking responses of this neuron model for the first time in this study. After the center frequency is determined, this approximation function is transferred into the ‘z’ domain by employing the Tustin discretization operator. This achieved discrete defined and fractional-order FHN neuron model becomes suitable for implementation on the digital platforms. To verify the proficiency of the proposed sweeping process experimentally, the fractional-order FHN model in ‘z’ domain is implemented on the FPGA platform. After these applications, the order of the approximation function is reduced to one. Once this followed frequency sweeping process is repeated for the first-order approximation, the fractional-order FHN neuron model, which is built by this least-order approximation function, is also implemented with the FPGA. Therefore, the reductions of the device utilization amounts by using this least-order approximation function and the importance of the specific frequency identification process are seen clearly.
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