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@ARTICLE{Senk:865395,
      author       = {Senk, Johanna and Korvasová, Karolína and Schuecker,
                      Jannis and Hagen, Espen and Tetzlaff, Tom and Diesmann,
                      Markus and Helias, Moritz},
      title        = {{C}onditions for wave trains in spiking neural networks},
      reportid     = {FZJ-2019-04880},
      year         = {2019},
      note         = {36 pages, 8 figures, 4 tables},
      abstract     = {Spatiotemporal patterns such as traveling waves are
                      frequently observed in recordings of neural activity. The
                      mechanisms underlying the generation of such patterns are
                      largely unknown. Previous studies have investigated the
                      existence and uniqueness of different types of waves or
                      bumps of activity using neural-field models,
                      phenomenological coarse-grained descriptions of
                      neural-network dynamics. But it remains unclear how these
                      insights can be transferred to more biologically realistic
                      networks of spiking neurons, where individual neurons fire
                      irregularly. Here, we employ mean-field theory to reduce a
                      microscopic model of leaky integrate-and-fire (LIF) neurons
                      with distance-dependent connectivity to an effective
                      neural-field model. In contrast to existing phenomenological
                      descriptions, the dynamics in this neural-field model
                      depends on the mean and the variance in the synaptic input,
                      both determining the amplitude and the temporal structure of
                      the resulting effective coupling kernel. For the
                      neural-field model we employ linear stability analysis to
                      derive conditions for the existence of spatial and temporal
                      oscillations and wave trains, that is, temporally and
                      spatially periodic traveling waves. We first prove that wave
                      trains cannot occur in a single homogeneous population of
                      neurons, irrespective of the form of distance dependence of
                      the connection probability. Compatible with the architecture
                      of cortical neural networks, wave trains emerge in
                      two-population networks of excitatory and inhibitory neurons
                      as a combination of delay-induced temporal oscillations and
                      spatial oscillations due to distance-dependent connectivity
                      profiles. Finally, we demonstrate quantitative agreement
                      between predictions of the analytically tractable
                      neural-field model and numerical simulations of both
                      networks of nonlinear rate-based units and networks of LIF
                      neurons.},
      cin          = {INM-6 / IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {574 - Theory, modelling and simulation (POF3-574) / PhD no
                      Grant - Doktorand ohne besondere Förderung
                      (PHD-NO-GRANT-20170405) / SMHB - Supercomputing and
                      Modelling for the Human Brain (HGF-SMHB-2013-2017) / HBP
                      SGA1 - Human Brain Project Specific Grant Agreement 1
                      (720270) / DFG project 233510988 - Mathematische
                      Modellierung der Entstehung und Suppression pathologischer
                      Aktivitätszustände in den Basalganglien-Kortex-Schleifen
                      (233510988) / ERS Seed Fund (ZUK2) - Exploratory Research
                      Space: Seed Fund (2) als Anschubfinanzierung zur Erforschung
                      neuer interdisziplinärer Ideen (ZUK2-SF) / HBP SGA2 - Human
                      Brain Project Specific Grant Agreement 2 (785907) /
                      Helmholtz Young Investigators Group
                      (HGF-YoungInvestigatorsGroup)},
      pid          = {G:(DE-HGF)POF3-574 / G:(DE-Juel1)PHD-NO-GRANT-20170405 /
                      G:(DE-Juel1)HGF-SMHB-2013-2017 / G:(EU-Grant)720270 /
                      G:(GEPRIS)233510988 / G:(DE-82)ZUK2-SF / G:(EU-Grant)785907
                      / G:(DE-HGF)HGF-YoungInvestigatorsGroup},
      typ          = {PUB:(DE-HGF)25},
      url          = {https://juser.fz-juelich.de/record/865395},
}