ArticleSIAM journal on applied dynamical systems2013
Locally Contractive Dynamics in Generalized Integrate-and-Fire Neurons.
Article in SIAM journal on applied dynamical systems, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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Who cites it
2 citing papers in PubMed.
- An Adaptive Generalized Leaky Integrate-and-Fire Model for Hippocampal CA1 Pyramidal Neurons and Interneurons.Bulletin of mathematical biology · 2023Article
- Synchronization of Electrically Coupled Resonate-and-Fire Neurons.SIAM journal on applied dynamical systems · 2019Article
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5 authors.
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Abstract
Integrate-and-fire models of biological neurons combine differential equations with discrete spike events. In the simplest case, the reset of the neuronal voltage to its resting value is the only spike event. The response of such a model to constant input injection is limited to tonic spiking. We here study a generalized model in which two simple spike-induced currents are added. We show that this neuron exhibits not only tonic spiking at various frequencies but also the commonly observed neuronal bursting. Using analytical and numerical approaches, we show that this model can be reduced to a one-dimensional map of the adaptation variable and that this map is locally contractive over a broad set of parameter values. We derive a sufficient analytical condition on the parameters for the map to be globally contractive, in which case all orbits tend to a tonic spiking state determined by the fixed point of the return map. We then show that bursting is caused by a discontinuity in the return map, in which case the map is
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