Akademik Veri Yönetim Sistemi
PAMUKKALE UNIVERSITY JOURNAL OF ENGINEERING SCIENCES-PAMUKKALE UNIVERSITESI MUHENDISLIK BILIMLERI DERGISI, cilt.28, sa.2, ss.248-254, 2022 (ESCI)
This study focuses on the fractional version of the FitzHugh-Nagumo (FHN) neuron model. Firstly, the stability analysis of the fractionalorder FHN neuron model has been performed and the minimum fractional degree, at which the system could exhibit dynamic behavior, has been determined. Then, the responses of the fractional-order FHN neuron model have been obtained using the Grunwald-Letnikov (G-L) fractional derivative method. This method is one of the methods used in the numerical analysis of the systems that are represented by fractional order. Thanks to the hardware solutions of neuron models; the responses of mathematically defined systems can be obtained in the form of real-time signals, the cell membrane properties of the neurons can be described electromechanically, and the parameters that affect the dynamic behavior of neurons can be associated with the characteristics of the electronic components used in hardware solutions. In this study, the circuit implementation of the fractionalorder FHN neuron model is emphasized in order to see the usability of fractional-order calculations in systems that are inspired by biology. In this context, the R-C mimetic circuits have been used instead of classical capacitor elements to compensate for the fractional order in the integrator circuits that are designed by using op-amp, resistor and capacitor elements for the hardware solutions of the differential equations. In the first stage of the design of these R-C imitation circuits, a third-order transfer function has been obtained by the Matsuda approximation method. This obtained transfer function has been transformed into FOSTER-I R-C network and it has been used instead of the classical capacitor element in the integrator blocks of the circuit that is designed by us for the circuit implementation solution of the integer-order FHN neuron model. Thus, an alternative approach for circuit solution of the fractional-order FHN neuron model has been introduced and the verification of this structure has been made by the SPICE circuit simulation.