Bifurcations of lurching waves in a thalamic neuronal network
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Author(s)
Wasylenko, Thomas Michael
Cisternas, Jaime E.
Laing, Carlo R.
Kevrekidis, Ioannis G.
Date Issued
December 2010
Journal
Biological Cybernetics
Publisher
Springer Science + Business Media B.V.
Citation
Wasylenko, Thomas M. et al. “Bifurcations of lurching waves in a thalamic neuronal network.” Biological Cybernetics 103 (2010): 447-462.
Version
Author's final manuscript
Abstract
We consider a two-layer, one-dimensional lattice of neurons; one layer consists of excitatory thalamocortical neurons, while the other is comprised of inhibitory reticular thalamic neurons. Such networks are known to support “lurching” waves, for which propagation does not appear smooth, but rather progresses in a saltatory fashion; these waves can be characterized by different spatial widths (different numbers of neurons active at the same time). We show that these lurching waves are fixed points of appropriately defined Poincaré maps, and follow these fixed points as parameters are varied. In this way, we are able to explain observed transitions in behavior, and, in particular, to show how branches with different spatial widths are linked with each other. Our computer-assisted analysis is quite general and could be applied to other spatially extended systems which exhibit this non-trivial form of wave propagation.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00422-010-0409-3
