Clarification and complement to ``Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons

DOI10.1186/s13408-015-0031-8zbMath1361.92014arXiv1412.7728OpenAlexW1897412463WikidataQ41920254 ScholiaQ41920254MaRDI QIDQ271660

Denis Talay, Olivier Faugeras, Mireille Bossy

Publication date: 7 April 2016

Published in: The Journal of Mathematical Neuroscience (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.7728

zbMATH Keywords

neural networks stochastic differential equations propagation of chaos Fitzhugh-Nagumo neurons Hodgkin-Huxley neurons mean-field limits neural assemblies

Mathematics Subject Classification ID

Neural biology (92C20) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (35)

Erratum to: ``Propagation of chaos in neural fields ⋮ Concentration Phenomena in Fitzhugh–Nagumo Equations: A Mesoscopic Approach ⋮ Optimal control of mean field equations with monotone coefficients and applications in neuroscience ⋮ A flexible split-step scheme for solving McKean-Vlasov stochastic differential equations ⋮ Mean field dynamics of a Wilson–Cowan neuronal network with nonlinear coupling term ⋮ Monotone convex order for the McKean-Vlasov processes ⋮ On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system ⋮ On uniform propagation of chaos ⋮ On a toy network of neurons interacting through their dendrites ⋮ Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions ⋮ Gaussian fluctuations for interacting particle systems with singular kernels ⋮ Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results ⋮ Distributed synaptic weights in a LIF neural network and learning rules ⋮ Strong convergence of Euler-Maruyama schemes for doubly perturbed McKean-Vlasov stochastic differential equations ⋮ Coherence resonance in neural networks: theory and experiments ⋮ Fluctuations for spatially extended Hawkes processes ⋮ Functional convex order for the scaled McKean-Vlasov processes ⋮ Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations ⋮ Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks ⋮ Concentration profiles in FitzHugh-Nagumo neural networks: a Hopf-Cole approach ⋮ Rigorous Derivation of the Nonlocal Reaction-Diffusion Fitzhugh--Nagumo System ⋮ Mean field limit for Coulomb-type flows ⋮ Quenched asymptotics for interacting diffusions on inhomogeneous random graphs ⋮ An adaptive Euler-Maruyama scheme for Mckean-Vlasov SDEs with super-linear growth and application to the mean-field Fitzhugh-Nagumo model ⋮ Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channels ⋮ Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo model ⋮ On explicit Milstein-type scheme for McKean-Vlasov stochastic differential equations with super-linear drift coefficient ⋮ Weakly interacting particle systems on inhomogeneous random graphs ⋮ Stability and prevalence of Mckean-Vlasov stochastic differential equations with non-Lipschitz coefficients ⋮ Clamping and Synchronization in the Strongly Coupled FitzHugh--Nagumo Model ⋮ Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction: a slow-fast dynamics approach ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications ⋮ Ensemble Kalman Sampler: Mean-field Limit and Convergence Analysis ⋮ Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift ⋮ The mean-field approximation for higher-dimensional Coulomb flows in the scaling-critical L ^∞ space

Cites Work

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