Conformable fractional-order derivate based adaptive FitzHugh-Nagumo neuron model

Ertuđrul Karakulak

   Various neuron models have been proposed and are extensively examined in the scientific literature. The FitzHugh-Nagumo neuron model is one of the most well-known and studied models. The FitzHugh-Nagumo model is not biologically consistent but operationally simple. A fractional-order derivative is described as a derivative with a non-integer order. Caputo, Grünwald-Letnikov, and Riemann-Liouville are some of the well-known fractional order derivatives. However, a simple fractional-order derivative called the conformable fractional-order derivative has been proposed in the literature and it is much simpler to use. In literature, there are already neuron models with fractional-order derivatives. In this study, a FitzHugh-Nagumo model circuit with a conformable fractional derivative capacitor and conformable fractional derivative inductor is proposed. The proposed circuit is modelled, and its simulation results are given. The simulation results reveal that the model circuit shows both slow and fast adaptation in firing frequency under sustained current stimulation.

Keywords: conformable fractional derivative, FitzHugh-Nagumo neuron model, neuron model, neural adaptation

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