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@ARTICLE{Stubenrauch:910246,
      author       = {Stubenrauch, Jakob and Keup, Christian and Kurth, Anno C.
                      and Helias, Moritz and van Meegen, Alexander},
      title        = {{P}hase {S}pace {A}nalysis of {C}haotic {N}eural
                      {N}etworks},
      publisher    = {arXiv},
      reportid     = {FZJ-2022-03707},
      year         = {2022},
      abstract     = {We analytically determine the distribution of fixed points
                      in a canonical model of a chaotic neural network. This
                      distribution reveals that fixed points and dynamics are
                      confined to separate shells in phase space. Furthermore, the
                      distribution enables us to determine the eigenvalue spectra
                      of the Jacobian at the fixed points. Perhaps
                      counter-intuitively, the velocity of the dynamics is
                      strongly correlated with the direction imposed by the
                      nearest fixed point despite the spatial separation. We
                      propose that this influence of the fixed points is mediated
                      by tangentially fixed lines.},
      keywords     = {Disordered Systems and Neural Networks (cond-mat.dis-nn)
                      (Other) / Chaotic Dynamics (nlin.CD) (Other) / FOS: Physical
                      sciences (Other)},
      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          = {5231 - Neuroscientific Foundations (POF4-523) / HBP SGA3 -
                      Human Brain Project Specific Grant Agreement 3 (945539) /
                      GRK 2416:  MultiSenses-MultiScales: Novel approaches to
                      decipher neural processing in multisensory integration
                      (368482240) / ACA - Advanced Computing Architectures
                      (SO-092) / RenormalizedFlows - Transparent Deep Learning
                      with Renormalized Flows (BMBF-01IS19077A) / SDS005 - Towards
                      an integrated data science of complex natural systems
                      (PF-JARA-SDS005) / PhD no Grant - Doktorand ohne besondere
                      Förderung (PHD-NO-GRANT-20170405) / MSNN - Theory of
                      multi-scale neuronal networks (HGF-SMHB-2014-2018)},
      pid          = {G:(DE-HGF)POF4-5231 / G:(EU-Grant)945539 /
                      G:(GEPRIS)368482240 / G:(DE-HGF)SO-092 /
                      G:(DE-Juel-1)BMBF-01IS19077A / G:(DE-Juel-1)PF-JARA-SDS005 /
                      G:(DE-Juel1)PHD-NO-GRANT-20170405 /
                      G:(DE-Juel1)HGF-SMHB-2014-2018},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2210.07877},
      url          = {https://juser.fz-juelich.de/record/910246},
}