MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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.

87.19.La, 05.45.-a, 87.10.+e
quasi-active dendrites, traveling waves, integrate-and-fire, kinematic

Related publications

2003 Repository Open Access
Matthew James, Steve Coombes and Paul Bressloff

Effects of quasiactive membrane on multiply periodic traveling waves in integrate-and-fire systems

In: The European physical journal / C, 67 (2003) 5, 051905-1 - 051905-6