A theoretical connection between the Noisy Leaky integrate-and-fire and the escape rate models: The non-autonomous case

Finding a mathematical model that incorporates various stochastic aspects of neural dynamics has proven to be a continuous challenge. Among the different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most popular. These two models are generally thought to...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2020, Vol.15, p.59
Main Authors: Dumont, Grégory, Henry, Jacques, Tarniceriu, Carmen Oana
Format: Article
Language:English
Subjects:
Mathematical models
Nervous system
Stochastic processes
Stochasticity
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Summary:Finding a mathematical model that incorporates various stochastic aspects of neural dynamics has proven to be a continuous challenge. Among the different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most popular. These two models are generally thought to express different noise action over the neural cell. In this paper we investigate the link between the two formalisms in the case of a neuron subject to a time dependent input. To this aim, we introduce a new general stochastic framework. As we shall prove, our general framework entails the two already existing ones. Our results have theoretical implications since they offer a general view upon the two stochastic processes mostly used in neuroscience, upon the way they can be linked, and explain their observed statistical similarity.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/2020017