000910246 001__ 910246 000910246 005__ 20240313103122.0 000910246 0247_ $$2doi$$a10.48550/ARXIV.2210.07877 000910246 0247_ $$2Handle$$a2128/32902 000910246 037__ $$aFZJ-2022-03707 000910246 1001_ $$0P:(DE-Juel1)188215$$aStubenrauch, Jakob$$b0$$eCorresponding author$$ufzj 000910246 245__ $$aPhase Space Analysis of Chaotic Neural Networks 000910246 260__ $$barXiv$$c2022 000910246 3367_ $$0PUB:(DE-HGF)25$$2PUB:(DE-HGF)$$aPreprint$$bpreprint$$mpreprint$$s1669884345_25750 000910246 3367_ $$2ORCID$$aWORKING_PAPER 000910246 3367_ $$028$$2EndNote$$aElectronic Article 000910246 3367_ $$2DRIVER$$apreprint 000910246 3367_ $$2BibTeX$$aARTICLE 000910246 3367_ $$2DataCite$$aOutput Types/Working Paper 000910246 520__ $$aWe analytically determine the distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore, the distribution enables us to determine the eigenvalue spectra of the Jacobian at the fixed points. Perhaps counter-intuitively, the velocity of the dynamics is strongly correlated with the direction imposed by the nearest fixed point despite the spatial separation. We propose that this influence of the fixed points is mediated by tangentially fixed lines. 000910246 536__ $$0G:(DE-HGF)POF4-5231$$a5231 - Neuroscientific Foundations (POF4-523)$$cPOF4-523$$fPOF IV$$x0 000910246 536__ $$0G:(EU-Grant)945539$$aHBP SGA3 - Human Brain Project Specific Grant Agreement 3 (945539)$$c945539$$fH2020-SGA-FETFLAG-HBP-2019$$x1 000910246 536__ $$0G:(GEPRIS)368482240$$aGRK 2416: MultiSenses-MultiScales: Novel approaches to decipher neural processing in multisensory integration (368482240)$$c368482240$$x2 000910246 536__ $$0G:(DE-HGF)SO-092$$aACA - Advanced Computing Architectures (SO-092)$$cSO-092$$x3 000910246 536__ $$0G:(DE-Juel-1)BMBF-01IS19077A$$aRenormalizedFlows - Transparent Deep Learning with Renormalized Flows (BMBF-01IS19077A)$$cBMBF-01IS19077A$$x4 000910246 536__ $$0G:(DE-Juel-1)PF-JARA-SDS005$$aSDS005 - Towards an integrated data science of complex natural systems (PF-JARA-SDS005)$$cPF-JARA-SDS005$$x5 000910246 536__ $$0G:(DE-Juel1)PHD-NO-GRANT-20170405$$aPhD no Grant - Doktorand ohne besondere Förderung (PHD-NO-GRANT-20170405)$$cPHD-NO-GRANT-20170405$$x6 000910246 536__ $$0G:(DE-Juel1)HGF-SMHB-2014-2018$$aMSNN - Theory of multi-scale neuronal networks (HGF-SMHB-2014-2018)$$cHGF-SMHB-2014-2018$$fMSNN$$x7 000910246 588__ $$aDataset connected to DataCite 000910246 650_7 $$2Other$$aDisordered Systems and Neural Networks (cond-mat.dis-nn) 000910246 650_7 $$2Other$$aChaotic Dynamics (nlin.CD) 000910246 650_7 $$2Other$$aFOS: Physical sciences 000910246 7001_ $$0P:(DE-Juel1)171384$$aKeup, Christian$$b1$$ufzj 000910246 7001_ $$0P:(DE-Juel1)176776$$aKurth, Anno C.$$b2$$ufzj 000910246 7001_ $$0P:(DE-Juel1)144806$$aHelias, Moritz$$b3$$ufzj 000910246 7001_ $$0P:(DE-Juel1)173607$$avan Meegen, Alexander$$b4$$ufzj 000910246 773__ $$a10.48550/ARXIV.2210.07877 000910246 8564_ $$uhttps://doi.org/10.48550/arXiv.2210.07877 000910246 8564_ $$uhttps://juser.fz-juelich.de/record/910246/files/2210.07877.pdf$$yOpenAccess 000910246 909CO $$ooai:juser.fz-juelich.de:910246$$pdnbdelivery$$pec_fundedresources$$pVDB$$pdriver$$popen_access$$popenaire 000910246 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)188215$$aForschungszentrum Jülich$$b0$$kFZJ 000910246 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)171384$$aForschungszentrum Jülich$$b1$$kFZJ 000910246 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)176776$$aForschungszentrum Jülich$$b2$$kFZJ 000910246 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)144806$$aForschungszentrum Jülich$$b3$$kFZJ 000910246 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)173607$$aForschungszentrum Jülich$$b4$$kFZJ 000910246 9131_ $$0G:(DE-HGF)POF4-523$$1G:(DE-HGF)POF4-520$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5231$$aDE-HGF$$bKey Technologies$$lNatural, Artificial and Cognitive Information Processing$$vNeuromorphic Computing and Network Dynamics$$x0 000910246 9141_ $$y2022 000910246 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000910246 9201_ $$0I:(DE-Juel1)INM-6-20090406$$kINM-6$$lComputational and Systems Neuroscience$$x0 000910246 9201_ $$0I:(DE-Juel1)IAS-6-20130828$$kIAS-6$$lTheoretical Neuroscience$$x1 000910246 9201_ $$0I:(DE-Juel1)INM-10-20170113$$kINM-10$$lJara-Institut Brain structure-function relationships$$x2 000910246 9801_ $$aFullTexts 000910246 980__ $$apreprint 000910246 980__ $$aVDB 000910246 980__ $$aUNRESTRICTED 000910246 980__ $$aI:(DE-Juel1)INM-6-20090406 000910246 980__ $$aI:(DE-Juel1)IAS-6-20130828 000910246 980__ $$aI:(DE-Juel1)INM-10-20170113 000910246 981__ $$aI:(DE-Juel1)IAS-6-20130828