One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise

DOI10.1137/140995738zbMath1352.37199arXiv1411.2273OpenAlexW2950854193MaRDI QIDQ3196649

Cheng Ly, Wilten Nicola, Sue Ann Campbell

Publication date: 30 October 2015

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.2273

zbMATH Keywords

neural networksbifurcation analysismean-field systemsmoment-closure reductionspopulation density equations

Mathematics Subject Classification ID

Neural biology (92C20) Dynamical systems in biology (37N25)

Related Items (4)

Variable synaptic strengths controls the firing rate distribution in feedforward neural networks ⋮ Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus ⋮ Firing rate dynamics in recurrent spiking neural networks with intrinsic and network heterogeneity ⋮ Nonsmooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons

Uses Software

• AUTO-86
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Cites Work

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• Bifurcations of large networks of two-dimensional integrate and fire neurons
• Spike-train spectra and network response functions for nonlinear integrate-and-fire neurons
• A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application in orientation tuning
• Nonsmooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons
• Stochastic Neural Field Theory and the System-Size Expansion
• Dynamics of the Firing Probability of Noisy Integrate-and-Fire Neurons
• Theory of Input Spike Auto- and Cross-Correlations and Their Effect on the Response of Spiking Neurons
• Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons
• Asynchronous States and the Emergence of Synchrony in Large Networks of Interacting Excitatory and Inhibitory Neurons
• Firing Rate of the Noisy Quadratic Integrate-and-Fire Neuron
• Systematic Fluctuation Expansion for Neural Network Activity Equations
• A Principled Dimension-Reduction Method for the Population Density Approach to Modeling Networks of Neurons with Synaptic Dynamics
• Critical Analysis of Dimension Reduction by a Moment Closure Method in a Population Density Approach to Neural Network Modeling
• MATCONT

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