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Neural Oscillators: Weak Coupling

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Mathematical Foundations of Neuroscience

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 35))

Abstract

This chapter begins the second part of the book. By now, we hope that the reader has a thorough knowledge of single cell dynamics and is ready to move onto networks. There are two main approaches to the analysis and modeling of networks of neurons. In one approach, the details of the action potentials (spikes) matter a great deal. In the second approach, we do not care about the timing of individual neurons; rather, we are concerned only with the firing rates of populations. This division is reflected in the sometimes acrimonious battles between those who believe that actual spike times matter and those who believe that the rates are all that the brain cares about. On these issues, we have our own opinions, but for the sake of the reader, we will remain agnostic and try to present both sorts of models.

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Authors and Affiliations

  1. Dept. Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania, 15260, USA

    G. Bard Ermentrout

  2. Dept. Mathematics, Ohio State University, 231 W. 18th Ave, Columbus, Ohio, 43210, USA

    David H. Terman

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  1. G. Bard Ermentrout
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  2. David H. Terman
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Correspondence to G. Bard Ermentrout .

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Ermentrout, G.B., Terman, D.H. (2010). Neural Oscillators: Weak Coupling. In: Mathematical Foundations of Neuroscience. Interdisciplinary Applied Mathematics, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87708-2_8

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