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Bifurcations of lurching waves in a thalamic neuronal network

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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.

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Author notes

  1. Thomas M. Wasylenko

    Present address: Department of Chemical Engineering, MIT, Cambridge, MA, 02139, USA

Authors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544, USA

    Thomas M. Wasylenko

  2. Facultad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Santiago, Chile

    Jaime E. Cisternas

  3. IIMS, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand

    Carlo R. Laing

  4. Department of Chemical Engineering and PACM, Princeton University, Princeton, NJ, 08544, USA

    Ioannis G. Kevrekidis

Authors
  1. Thomas M. Wasylenko
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  2. Jaime E. Cisternas
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  3. Carlo R. Laing
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  4. Ioannis G. Kevrekidis
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Corresponding author

Correspondence to Carlo R. Laing.

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Wasylenko, T.M., Cisternas, J.E., Laing, C.R. et al. Bifurcations of lurching waves in a thalamic neuronal network. Biol Cybern 103, 447–462 (2010). https://doi.org/10.1007/s00422-010-0409-3

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  • DOI: https://doi.org/10.1007/s00422-010-0409-3

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