ArticleJournal of computational neuroscience2013
Bifurcations of large networks of two-dimensional integrate and fire neurons.
Article in Journal of computational neuroscience, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- Biophysically inspired mean-field model of neuronal populations driven by ion-exchange mechanisms.eLife · 2026Article
- Neural heterogeneity as a unifying mechanism for efficient learning in spiking neural networks.Frontiers in computational neuroscience · 2025Article
- Anti-Disturbance of Scale-Free Spiking Neural Network against Impulse Noise.Brain sciences · 2023Article
- Exact mean-field models for spiking neural networks with adaptation.Journal of computational neuroscience · 2022Article
- A Rate-Reduced Neuron Model for Complex Spiking Behavior.Journal of mathematical neuroscience · 2017Article
- Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures.Journal of computational neuroscience · 2016Article
- Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights.Frontiers in computational neuroscience · 2016Article
- Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus.Journal of computational neuroscience · 2015Article
- Dynamics of the exponential integrate-and-fire model with slow currents and adaptation.Journal of computational neuroscience · 2014Article
- Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context.F1000Research · 2014Article
- Analytical approximations of the firing rate of an adaptive exponential integrate-and-fire neuron in the presence of synaptic noise.Frontiers in computational neuroscience · 2014Article
- Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons.Frontiers in computational neuroscience · 2013Article
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2 authors.
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Abstract
Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math 68(4):1045-1079, 2008). However, when the models are coupled together to form networks, the networks can display bifurcations that an uncoupled oscillator cannot. For example, the networks can transition from firing with a constant rate to burst firing. This paper introduces a technique to reduce a full network of this class of neurons to a mean field model, in the form of a system of switching ordinary differential equations. The reduction uses population density methods and a quasi-steady state approximation to arrive at the mean field system. Reduced models are derived for networks with different topologies and different model neurons with biologically derived parameters. The mean field equations are able to qualitatively and quantitatively describe the bifurcations that the full networks display. Extensions and higher order approximations are discussed.
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