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On bifurcations and chaos in random neural networks

On bifurcations and chaos in random neural networks Chaos in nervous system is a fascinating but controversial field of investigation. To approach the role of chaos in the real brain, we theoretically and numerically investigate the occurrence of chaos inartificial neural networks. Most of the time, recurrent networks (with feedbacks) are fully connected. This architecture being not biologically plausible, the occurrence of chaos is studied here for a randomly diluted architecture. By normalizing the variance of synaptic weights, we produce a bifurcation parameter, dependent on this variance and on the slope of the transfer function, that allows a sustained activity and the occurrence of chaos when reaching a critical value. Even for weak connectivity and small size, we find numerical results in accordance with the theoretical ones previously established for fully connected infinite sized networks. The route towards chaos is numerically checked to be a quasi-periodic one, whatever the type of the first bifurcation is. Our results suggest that such high-dimensional networks behave like low-dimensional dynamical systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

On bifurcations and chaos in random neural networks

Doyon, B.; Cessac, B.; Quoy, M.; Samuelides, M.
Acta Biotheoretica , Volume 42 (3) – Nov 13, 2004
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References (13)

Publisher
Springer Journals
Copyright
Copyright
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/BF00709492
Publisher site
See Article on Publisher Site

Abstract

Chaos in nervous system is a fascinating but controversial field of investigation. To approach the role of chaos in the real brain, we theoretically and numerically investigate the occurrence of chaos inartificial neural networks. Most of the time, recurrent networks (with feedbacks) are fully connected. This architecture being not biologically plausible, the occurrence of chaos is studied here for a randomly diluted architecture. By normalizing the variance of synaptic weights, we produce a bifurcation parameter, dependent on this variance and on the slope of the transfer function, that allows a sustained activity and the occurrence of chaos when reaching a critical value. Even for weak connectivity and small size, we find numerical results in accordance with the theoretical ones previously established for fully connected infinite sized networks. The route towards chaos is numerically checked to be a quasi-periodic one, whatever the type of the first bifurcation is. Our results suggest that such high-dimensional networks behave like low-dimensional dynamical systems.

Journal

Acta Biotheoretica – Springer Journals

Published: Nov 13, 2004

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