Neural Oscillators: Weak Coupling

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


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.


Hopf Bifurcation Rotation Number Inhibitory Cell Spiral Wave Excitatory Cell 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Dept. MathematicsOhio State UniversityColumbusUSA

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