MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) 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.
The effects of quasi-active membrane on multiply periodic traveling waves in integrate-and-fire systems
Matthew James, Steve Coombes and Paul BressloffAbstract
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.
- Received:
- 10.09.02
- Published:
- 10.09.02
- PACS:
- 87.19.La, 05.45.-a, 87.10.+e
- Keywords:
- quasi-active dendrites, traveling waves, integrate-and-fire, kinematic