Dynamics of globally delay-coupled neurons displaying subthreshold oscillations
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We study an ensemble of neurons that are coupled through their time-delayed collective mean field. The individual neuron is modelled using a Hodgkin–Huxley-type conductance model with parameters chosen such that the uncoupled neuron displays autonomous subthreshold oscillations of the membrane potential. We find that the ensemble generates a rich variety of oscillatory activities that are mainly controlled by two time scales: the natural period of oscillation at the single neuron level and the delay time of the global coupling. When the neuronal oscillations are synchronized, they can be either in-phase or out-of-phase. The phase-shifted activity is interpreted as the result of a phase-flip bifurcation, also occurring in a set of globally delay-coupled limit cycle oscillators. At the bifurcation point, there is a transition from in-phase to out-of-phase (or vice versa) synchronized oscillations, which is accompanied by an abrupt change in the common oscillation frequency. This phase-flip bifurcation was recently investigated in two mutually delay-coupled oscillators and can play a role in the mechanisms by which the neurons switch among different firing patterns.
CitationMasoller, C.; Torrent, M.C.; Garcia-Ojalvo, J. Dynamics of globally delay-coupled neurons displaying subthreshold oscillations. "Philosophical transactions of the Royal Society of London. Series A, mathematical and physical sciences", Agost 2009, vol. 367, p. 3255-3266.
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