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Journal of Computational Neuroscience

, Volume 18, Issue 3, pp 265–274 | Cite as

The Onset and Extinction of Neural Spiking: A Numerical Bifurcation Approach

  • W. GovaertsEmail author
  • B. Sautois
Article

Abstract

We study the onset of neural spiking when the equilibrium rest state loses stability by the change of a critical parameter, the applied current. In the case of the well-known Morris-Lecar model, we start from a complete numerical study of the bifurcation diagram in the most relevant two-parameter range. This diagram includes all equilibrium and limit cycle bifurcations, thus correcting and completing earlier studies.

We discuss and classify the behavior of the spiking orbits, when increasing or decreasing the applied current. A complete classification can be extracted from the complete bifurcation diagram. It is based on three components: bifurcation type of the equilibrium at the loss of stability, subcritical behavior in the limit of decreasing the applied current and supercritical behavior in the limit of increasing the applied current.

Keywords

neural models Morris-Lecar classification spiking 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceGhent UniversityGhentBelgium

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