Preprint

FZJ-2022-03707

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Phase Space Analysis of Chaotic Neural Networks

Stubenrauch, J. (Corresponding author)FZJ* ; Keup, C.FZJ* ; Kurth, A. C.FZJ* ; Helias, M.FZJ* ; van Meegen, A.FZJ*

2022
arXiv

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Please use a persistent id in citations: http://hdl.handle.net/2128/32902  doi:10.48550/ARXIV.2210.07877

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.

Keyword(s): Disordered Systems and Neural Networks (cond-mat.dis-nn) ; Chaotic Dynamics (nlin.CD) ; FOS: Physical sciences

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Contributing Institute(s):

1. Computational and Systems Neuroscience (INM-6)
2. Theoretical Neuroscience (IAS-6)
3. Jara-Institut Brain structure-function relationships (INM-10)

Research Program(s):

1. 5231 - Neuroscientific Foundations (POF4-523) (POF4-523)
2. HBP SGA3 - Human Brain Project Specific Grant Agreement 3 (945539) (945539)
3. GRK 2416:  MultiSenses-MultiScales: Novel approaches to decipher neural processing in multisensory integration (368482240) (368482240)
4. ACA - Advanced Computing Architectures (SO-092) (SO-092)
5. RenormalizedFlows - Transparent Deep Learning with Renormalized Flows (BMBF-01IS19077A) (BMBF-01IS19077A)
6. SDS005 - Towards an integrated data science of complex natural systems (PF-JARA-SDS005) (PF-JARA-SDS005)
7. PhD no Grant - Doktorand ohne besondere Förderung (PHD-NO-GRANT-20170405) (PHD-NO-GRANT-20170405)
8. MSNN - Theory of multi-scale neuronal networks (HGF-SMHB-2014-2018) (HGF-SMHB-2014-2018)

Appears in the scientific report 2022

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Database coverage:

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