Nonlinear dynamics analysis of a self-organizing recurrent neural network : chaos waning

  • Self-organization is thought to play an important role in structuring nervous systems. It frequently arises as a consequence of plasticity mechanisms in neural networks: connectivity determines network dynamics which in turn feed back on network structure through various forms of plasticity. Recently, self-organizing recurrent neural network models (SORNs) have been shown to learn non-trivial structure in their inputs and to reproduce the experimentally observed statistics and fluctuations of synaptic connection strengths in cortex and hippocampus. However, the dynamics in these networks and how they change with network evolution are still poorly understood. Here we investigate the degree of chaos in SORNs by studying how the networks' self-organization changes their response to small perturbations. We study the effect of perturbations to the excitatory-to-excitatory weight matrix on connection strengths and on unit activities. We find that the network dynamics, characterized by an estimate of the maximum Lyapunov exponent, becomes less chaotic during its self-organization, developing into a regime where only few perturbations become amplified. We also find that due to the mixing of discrete and (quasi-)continuous variables in SORNs, small perturbations to the synaptic weights may become amplified only after a substantial delay, a phenomenon we propose to call deferred chaos.

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Author:Jürgen Eser, Pengsheng Zheng, Jochen TrieschORCiD
Pubmed Id:
Parent Title (English):PLoS One
Place of publication:Lawrence, Kan.
Document Type:Article
Date of Publication (online):2014/01/23
Date of first Publication:2014/01/23
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2014/01/29
Page Number:9
Copyright: © 2014 Eser et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Institutes:Wissenschaftliche Zentren und koordinierte Programme / Frankfurt Institute for Advanced Studies (FIAS)
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoCreative Commons - Namensnennung 4.0