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Traveling Waves of Excitation in Neural Field Models: Equivalence of Rate Descriptions and Integrate-and-Fire Dynamics

cremers{at}uni-mannheim.de, Department of Mathematics and Computer Science, University of Mannheim, 68131 Mannheim, Germany

Andreas V. M. Herz

a.herz{at}biologie.hu-berlin.de, Innovationskolleg Theoretische Biologie, Humboldt-Universität zu Berlin, 10115 Berlin, Germany

Field models provide an elegant mathematical framework to analyze large-scale patterns of neural activity. On the microscopic level, these models are usually based on either a firing-rate picture or integrate-and-fire dynamics. This article shows that in spite of the large conceptual differences between the two types of dynamics, both generate closely related plane-wave solutions. Furthermore, for a large group of models, estimates about the network connectivity derived from the speed of these plane waves only marginally depend on the assumed class of microscopic dynamics. We derive quantitative results about this phenomenon and discuss consequences for the interpretation of experimental data.

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