Journal article
Mechanisms for Frequency Control in Neuronal Competition Models
SIAM journal on applied dynamical systems, Vol.7(2), pp.609-649
2008
DOI: 10.1137/070705842
PMCID: PMC2954747
PMID: 20953287
Abstract
We investigate analytically a firing rate model for a two-population network based on mutual inhibition and slow negative feedback in the form of spike frequency adaptation. Both neuronal populations receive external constant input whose strength determines the system’s dynamical state—a steady state of identical activity levels or periodic oscillations or a winner-take-all state of bistability. We prove that oscillations appear in the system through supercritical Hopf bifurcations and that they are antiphase. The period of oscillations depends on the input strength in a nonmonotonic fashion, and we show that the increasing branch of the period versus input curve corresponds to a release mechanism and the decreasing branch to an escape mechanism. In the limiting case of infinitely slow feedback we characterize the conditions for release, escape, and occurrence of the winner-take-all behavior. Some extensions of the model are also discussed.
Details
- Title: Subtitle
- Mechanisms for Frequency Control in Neuronal Competition Models
- Creators
- Rodica Curtu - )Asya Shpiro - )Nava Rubin - )John Rinzel - )
- Resource Type
- Journal article
- Publication Details
- SIAM journal on applied dynamical systems, Vol.7(2), pp.609-649
- DOI
- 10.1137/070705842
- PMID
- 20953287
- PMCID
- PMC2954747
- NLM abbreviation
- SIAM J Appl Dyn Syst
- ISSN
- 1536-0040
- eISSN
- 1536-0040
- Language
- English
- Date published
- 2008
- Academic Unit
- Iowa Neuroscience Institute; Mathematics
- Record Identifier
- 9983985704202771
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