Coupled fractional spiking neurons - Pinto, Carla M.A. (2016)
We propose a fractional-order (FO) model of two symmetrically coupled Hodgkin-Huxley equations and study the patterns of the neurons’ firing rates, for distinct values of the order of the fractional derivative, , and the temperature, . We find that, for positive values of the coupling, the neurons exhibit in-phase periodic solutions (neurons fire at the same time). Moreover, the spike amplitude decreases with , meaning that the neuron stops firing below some threshold. This is observed for the three values of studied here. For smaller , the periodic solutions are sustained for smaller values of . For negative values of the coupling the neurons show anti-phase synchronization for the integer-order model (neurons fire periodically with a halfperiod phase shift). In the case of the FO model, these antiphase symmetric solutions disappear as decreases from 1, for fixed . Another bifurcation seems thus to occur being again a bifurcation parameter. This feature occurs only in the FO system, which seems to behave as an asymmetrically coupled HH system previously studied. Furher analyses is required.