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Abstract(s)
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, 𝛼, and the temperature, 𝑇.
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 𝛼, meaning that
the neuron stops firing below some threshold. This is observed
for the three values of 𝑇 studied here. For smaller 𝑇, the periodic
solutions are sustained for smaller values of 𝛼. 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 𝛼 decreases from 1, for
fixed 𝑇. Another bifurcation seems thus to occur being 𝛼 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.
Description
Keywords
Mathematical model Neurons Synchronization Bifurcation Couplings Biological system modeling Orbits
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Citation
Publisher
Institute of Electrical and Electronics Engineers