ArticleFrontiers in computational neuroscience2013
Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons.
Article in Frontiers in computational neuroscience, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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14 citing papers in PubMed.
- Neural heterogeneity as a unifying mechanism for efficient learning in spiking neural networks.Frontiers in computational neuroscience · 2025Article
- Exact mean-field models for spiking neural networks with adaptation.Journal of computational neuroscience · 2022Article
- Toward a multiscale modeling framework for understanding serotonergic function.Journal of psychopharmacology (Oxford, England) · 2017Review
- Effects of ion channel noise on neural circuits: an application to the respiratory pattern generator to investigate breathing variability.Journal of neurophysiology · 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
- Experimentally Verified Parameter Sets for Modelling Heterogeneous Neocortical Pyramidal-Cell Populations.PLoS computational biology · 2015Article
- Improper activation of D1 and D2 receptors leads to excess noise in prefrontal cortex.Frontiers in computational neuroscience · 2015Article
- Differential effects of excitatory and inhibitory heterogeneity on the gain and asynchronous state of sparse cortical networks.Frontiers in computational neuroscience · 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
- From neuronal populations to behavior: a computational journey.Frontiers in computational neuroscience · 2014Article
- Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context.F1000Research · 2014Article
- Subtractive, divisive and non-monotonic gain control in feedforward nets linearized by noise and delays.Frontiers in computational neuroscience · 2014Article
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Abstract
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons.
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