Effects of quasiactive membrane on multiply periodic traveling waves in integrate-and-fire systems
We consider the dynamics of a one-dimensional continuum of
synaptically-interacting integrate-and-fire neurons with
realistic forms of axo-dendritic interaction. The
speed and stability of traveling waves is investigated as a
function of discrete communication delays, distributed synaptic
delays and axo-dendritic delays arising from the spatially
extended nature of the model neuron. In particular, dispersion
curves for periodic traveling waves are constructed. Nonlinear
ionic channels in the dendrite responsible for a so-called
quaisactive bandpass response are shown to significantly
influence the shape of dispersion curves. Moreover, a
kinematic theory of spike train propagation suggests that period
doubling bifurcations of a singly periodic wave can occur in
dendritic systems with quasi-active membrane. The explicit
construction of period doubled solutions is used to confirm this
prediction.
University of Utah
| Department of Mathematics
|
bressloff@math.utah.edu
Aug 2001.