Dynamical characteristics of the fractional-order FitzHugh-Nagumo model neuron and its synchronization

Through the research on the fractional-order FitzHugh-Nagumo model neuron, it is found that the Hopf bifurcation point of the fractional-order model, where the state of the model neuron changes from quiescence to periodic spiking, is different from that of the corresponding integer-order model when the externally applied current is considered as the bifurcation parameter. We further demonstrate that the range of the strength of the externally applied current in the fractional-order model neuron, which can make the model neuron exhibit periodic spiking, is smaller than that in the corresponding integer-order model neuron. However, the firing frequency of the fractional-order model neuron is higher than that of the integer-order counterpart. Meanwhile, we show that the synchronization rate of two electrically coupled fractional-order FitzHugh-Nagumo model neurons is greater than that of the integer-order counterpart. The Adomian decomposition method is employed to calculate fractional-order differential equations numerically because of its rapid convergence and high accuracy.