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Bulletin of Mathematical Biology

, Volume 62, Issue 3, pp 467–481 | Cite as

Integrate-and-fire models with nonlinear leakage

  • Jianfeng Feng
  • David Brown
Article

Abstract

Can we express biophysical neuronal models as integrate-and-fire (IF) models with leakage coefficients which are no longer constant, as in the conventional leaky IF model, but functions of membrane potential and other biophysical variables? We illustrate the answer to this question using the FitzHugh-Nagumo (FHN) model as an example. A novel IF type model, the IF-FHN model, which approximates to the FHN model, is obtained. The leakage coefficient derived in the IF-FHN model has nonmonotonic relationship with membrane potential, revealing at least in part the intrinsic mechanisms underlying the FHN models. The IF-FHN model correspondingly exhibits more complex behaviour than the standard IF model. For example, in some parameter regions, the IF-FHN model has a coefficient of variation of the output interspike interval which is independent of the number of inhibitory inputs, being close to unity over the whole range, comparable to the FHN model as we noted previously (Brown et al., 1999).

Keywords

Membrane Potential Spike Train Synaptic Input Inhibitory Input Incoming Signal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Society for Mathematical Biology 2000

Authors and Affiliations

  • Jianfeng Feng
    • 1
  • David Brown
    • 1
  1. 1.Computational Neuroscience LaboratoryThe Babraham InstituteCambridgeUK

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