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The effects of quasi-active membrane on multiply periodic traveling waves in integrate-and-fire systems
Matthew James, Steve Coombes and Paul Bressloff
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 are 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 quasi-active 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.