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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.
Distributed transmission speeds and their effects on propagating activity in neural populations
Axel Hutt and Fatihcan M. AtayAbstract
Motivated by experimental evidence, a distribution of axonal transmission speeds is introduced into a standard field model of neural populations. The resulting field dynamics are analytically studied by a systematic investigation of the stability and bifurcations of equilibrium solutions. Using a perturbation approach, the effect of distributed speeds on bifurcations of equilibria are determined for general connectivity and speed distributions. In addition, a nonlinear analysis of traveling fronts is given. It is shown that the variance of the speed distribution affects the frequency of bifurcating periodic solutions and the phase speed of traveling waves.
- Received:
- 11.09.05
- Published:
- 11.09.05
- PACS:
- 87.18.Hf, 02.60.Nm, 87.19.La