Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities |
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Authors: | Srdjan Ostojic Nicolas Brunel and Vincent Hakim |
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Institution: | (1) Laboratoire de Physique Statistique, CNRS UMR 8550, Ecole Normale Supérieure, 75231 Paris Cedex 05, France;(2) Laboratory of Neurophysics and Physiology, CNRS UMR 8119, Université Paris Descartes, Paris, France |
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Abstract: | We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject
to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony
can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory
state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of
the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf
bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical
bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where
all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the
synchronization in an asynchronous network via a resonance at the firing-rate frequency.
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Keywords: | Gap junctions Oscillations Neural networks |
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