ArticleCommunications on pure and applied mathematics2013
Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection.
Article in Communications on pure and applied mathematics, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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10 citing papers in PubMed.
- The Emergence of a Universal Rhythmic Feature: Simple Models Can Produce Categorical Rhythms.Annals of the New York Academy of Sciences · 2026Article
- Deterministic, stochastic, and mean-field PDE models in neuroscience.Frontiers in computational neuroscience · 2026Review
- A cubic-quadratic phenomenological model explains the spiking, chaotic and bursting behaviors of neuron.Scientific reports · 2025Article
- Structure and dynamics that specialize neurons for high-frequency coincidence detection in the barn owl nucleus laminaris.Biological cybernetics · 2023Article
- Excitability and Threshold Mechanism for Enhanced Neuronal Response Induced by Inhibition Preceding Excitation.Neural plasticity · 2021Article
- Soma-axon coupling configurations that enhance neuronal coincidence detection.PLoS computational biology · 2019Article
- A biophysical modelling platform of the cochlear nucleus and other auditory circuits: From channels to networks.Hearing research · 2018Article
- A Single Differential Equation Description of Membrane Properties Underlying the Action Potential and the Axon Electric Field.Journal of electrical bioimpedance · 2018Article
- Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both.Frontiers in computational neuroscience · 2017Article
- Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience.Journal of mathematical neuroscience · 2016Article
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2 authors.
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Abstract
We review some widely studied models and firing dynamics for neuronal systems, both at the single cell and network level, and dynamical systems techniques to study them. In particular, we focus on two topics in mathematical neuroscience that have attracted the attention of mathematicians for decades: single-cell excitability and bursting. We review the mathematical framework for three types of excitability and onset of repetitive firing behavior in single-neuron models and their relation with Hodgkin's classification in 1948 of repetitive firing properties. We discuss the mathematical dissection of bursting oscillations using fast/slow analysis and demonstrate the approach using single-cell and mean-field network models. Finally, we illustrate the properties of Type III excitability in which case repetitive firing for constant or slow inputs is absent. Rather, firing is in response only to rapid enough changes in the stimulus. Our case study involves neuronal computations for sound localization for which neurons in the auditory brain stem perform extraordinarily precise coincidence detection with submillisecond temporal resolution.
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