This paper studies the famous Fitzhugh-Nagumo and Izhikevich neuron models in the fractional-order domain. Generalization of the integer models into the fractional-order domain providing a wider scope understanding of the neuron systems. The fractional Fitzhugh-Nagumo circuit model and the state space equations are introduced. Different fractional orders are studied as an example. Numerical solutions of the systems are given using non-standard finite difference scheme together with Grunwald-Letnikov discretization technique which is computationally efficient and accurate. The two models are compared and their behaviors are investigated at different fractional orders. © 2016 IEEE.
Armanyos M., Radwan A.G.
Fitzhugh model; Fractional order; Grunwald-Letnikov; Izhikevich model; non-standard finite difference
2016 13th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, ECTI-CON 2016, Art. No. 7561406, Doi: 10.1109/ECTICon.2016.7561406