Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

  • Srdjan OstojicEmail author
  • Nicolas Brunel
  • Vincent Hakim


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.


Gap junctions Oscillations Neural networks 



This work was supported by the Agence Nationale de la Recherche grant ANR-05-NEUR-030.


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Laboratoire de Physique Statistique, CNRS UMR 8550Ecole Normale SupérieureParis Cedex 05France
  2. 2.Laboratory of Neurophysics and Physiology, CNRS UMR 8119Université Paris DescartesParisFrance

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