Bifurcations of lurching waves in a thalamic neuronal network

Thomas M. Wasylenko, Jaime E. Cisternas, Carlo R. Laing, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

7 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)447-462
Number of pages16
JournalBiological Cybernetics
Volume103
Issue number6
DOIs
StatePublished - Dec 1 2010

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Computer Science(all)

Keywords

  • Bifurcation
  • Lattice
  • Lurching
  • RE-TC

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    Wasylenko, T. M., Cisternas, J. E., Laing, C. R., & Kevrekidis, I. G. (2010). Bifurcations of lurching waves in a thalamic neuronal network. Biological Cybernetics, 103(6), 447-462. https://doi.org/10.1007/s00422-010-0409-3