Transitions between asynchronous and synchronous states: a theory of correlations in small neural circuits

DOI10.1007/s10827-017-0667-3zbMath1402.92083OpenAlexW2755354344WikidataQ47847253 ScholiaQ47847253MaRDI QIDQ1628206

Anna Cattani, Stefano Panzeri, Diego Fasoli

Publication date: 4 December 2018

Published in: Journal of Computational Neuroscience (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10827-017-0667-3

zbMATH Keywords

bifurcation analysispropagation of chaosfinite-size effectsstochastic neural networkscritical slowing downgraded firing-rate modelsynchronous and asynchronous states

Mathematics Subject Classification ID

Neural biology (92C20)

Related Items (5)

Mean field analysis of large-scale interacting populations of stochastic conductance-based spiking neurons using the Klimontovich method ⋮ Bifurcation Analysis of Wilson-Cowan Model with Singular Impulses ⋮ Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model ⋮ Mathematical studies of the dynamics of finite-size binary neural networks: a review of recent progress ⋮ The Effect of Inhibitory Neurons on a Class of Neural Networks

Cites Work

• A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model
• Elements of applied bifurcation theory.
• Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons
• A mathematical framework for critical transitions: normal forms, variance and applications
• Stochastic Neural Field Theory and the System-Size Expansion
• Noise-Induced Behaviors in Neural Mean Field Dynamics
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