TY - JOUR
T1 - Bifurcations of lurching waves in a thalamic neuronal network
AU - Wasylenko, Thomas M.
AU - Cisternas, Jaime E.
AU - Laing, Carlo R.
AU - Kevrekidis, Ioannis G.
PY - 2010/12
Y1 - 2010/12
N2 - 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.
AB - 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.
KW - Bifurcation
KW - Lattice
KW - Lurching
KW - RE-TC
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U2 - 10.1007/s00422-010-0409-3
DO - 10.1007/s00422-010-0409-3
M3 - Article
C2 - 21140272
AN - SCOPUS:79151479229
SN - 0340-1200
VL - 103
SP - 447
EP - 462
JO - Biological Cybernetics
JF - Biological Cybernetics
IS - 6
ER -