TY - GEN
T1 - Bifurcation analysis of a thalamic relay neuron model
AU - Yin, Huibing
AU - Cox, Charles L.
AU - Mehta, Prashant G.
AU - Shanbhag, Uday V.
PY - 2009/11/23
Y1 - 2009/11/23
N2 - Thalamus is concerned with the relay of visual information from the retina to the visual cortex. Interestingly, the information transfer is strongly mediated by nonlinear dynamics of the neurons. In particular, experiments have shown that the thalamic neurons process visual input in two distinct nonlinear dynamic modes, the so-called tonic mode and the burst mode. This paper is concerned with a bifurcation analysis of the Hodgkin-Huxley type models of thalamic neurons. The analysis is used to show that the tonic mode arises as a type of global bifurcation where a homoclinic orbit interacts with a saddle node bifurcation in equilibria. Such a bifurcation is very efficient at the kind of rate coding that has been experimentally observed in the tonic mode. The burst mode is consistent with a subcritical Hopf bifurcation in slow currents. Finally, for both modes, the electrophysiological role of the so-called slow and fast currents is also discussed.
AB - Thalamus is concerned with the relay of visual information from the retina to the visual cortex. Interestingly, the information transfer is strongly mediated by nonlinear dynamics of the neurons. In particular, experiments have shown that the thalamic neurons process visual input in two distinct nonlinear dynamic modes, the so-called tonic mode and the burst mode. This paper is concerned with a bifurcation analysis of the Hodgkin-Huxley type models of thalamic neurons. The analysis is used to show that the tonic mode arises as a type of global bifurcation where a homoclinic orbit interacts with a saddle node bifurcation in equilibria. Such a bifurcation is very efficient at the kind of rate coding that has been experimentally observed in the tonic mode. The burst mode is consistent with a subcritical Hopf bifurcation in slow currents. Finally, for both modes, the electrophysiological role of the so-called slow and fast currents is also discussed.
UR - http://www.scopus.com/inward/record.url?scp=70449686759&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70449686759&partnerID=8YFLogxK
U2 - 10.1109/ACC.2009.5160443
DO - 10.1109/ACC.2009.5160443
M3 - Conference contribution
AN - SCOPUS:70449686759
SN - 9781424445240
T3 - Proceedings of the American Control Conference
SP - 337
EP - 342
BT - 2009 American Control Conference, ACC 2009
T2 - 2009 American Control Conference, ACC 2009
Y2 - 10 June 2009 through 12 June 2009
ER -