Asymptotic limit of a spatially-extended mean-field FitzHugh–Nagumo model

DOI10.1142/S0218202520500207zbMath1444.35139arXiv1906.08073OpenAlexW3006902759MaRDI QIDQ5128712

Joachim Crevat

Publication date: 23 October 2020

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.08073

zbMATH Keywords

neural networkasymptotic limitmodulated energyFitzHugh-Nagumo

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Reaction-diffusion equations (35K57) Neural networks for/in biological studies, artificial life and related topics (92B20) PDEs in connection with biology, chemistry and other natural sciences (35Q92)

Related Items (1)

Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions

Cites Work

• Unnamed Item
• Unnamed Item
• Mean field limit for disordered diffusions with singular interactions
• The second law of thermodynamics and stability
• A geometric approach to singular perturbation problems with applications to nerve impulse equations
• A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment
• Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channels
• Derivation of a voltage density equation from a voltage-conductance kinetic model for networks of integrate-and-fire neurons
• Mean-field limit of a spatially-extended Fitzhugh-Nagumo neural network
• Heteroclinic solutions of a van der Waals model with infinite nonlocal interactions
• Asymptotic analysis of Vlasov-type equations under strong local alignment regime
• Traveling Pulse Solutions for the Discrete FitzHugh–Nagumo System
• Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
• Traveling Waves of Bistable Dynamics on a Lattice
• On a relaxation approximation of the incompressible Navier-Stokes equations
• Rigorous Derivation of the Nonlocal Reaction-Diffusion Fitzhugh--Nagumo System
• Wave train selection by invasion fronts in the FitzHugh–Nagumo equation
• Stability of pulse solutions for the discrete FitzHugh–Nagumo system
• convergence of the vlasov-poisson system to the incompressible euler equations
• Clamping and Synchronization in the Strongly Coupled FitzHugh--Nagumo Model
• Hydrodynamic limit of the kinetic Cucker–Smale flocking model

This page was built for publication: Asymptotic limit of a spatially-extended mean-field FitzHugh–Nagumo model