Convergence towards equilibrium for a model with partial diffusion

DOI10.1080/03605302.2024.2344806zbMath1546.35241MaRDI QIDQ6595124

Delphine Salort, Didier Smets

Publication date: 29 August 2024

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Neural networks for/in biological studies, artificial life and related topics (92B20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Neural nets applied to problems in time-dependent statistical mechanics (82C32) Fokker-Planck equations (35Q84)

Cites Work

• On a toy model of interacting neurons
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Analysis of nonlinear noisy integrate \& fire neuron models: blow-up and steady states
• Towards a further understanding of the dynamics in the excitatory NNLIF neuron model: blow-up and global existence
• Hypocoercivity of linear kinetic equations via Harris's theorem
• Hypocoercivity without confinement
• Hopf bifurcation in a mean-field model of spiking neurons
• Long time behavior of a mean-field model of interacting neurons
• Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
• On a voltage-conductance kinetic system for integrate \& fire neural networks
• Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model
• Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience
• Spectral Gap for the Growth-Fragmentation Equation via Harris's Theorem
• Hypocoercivity
• Asymptotic behaviour of neuron population models structured by elapsed-time
• Rigorous Derivation of the Nonlocal Reaction-Diffusion Fitzhugh--Nagumo System
• Classical Solutions for a Nonlinear Fokker-Planck Equation Arising in Computational Neuroscience
• A multiple time renewal equation for neural assemblies with elapsed time model
• Long Time Behavior of an Age- and Leaky Memory-Structured Neuronal Population Equation
• The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states
• Global-in-time solutions and qualitative properties for the NNLIF neuron model with synaptic delay
• Hypocoercivity for linear kinetic equations conserving mass
• Dynamics of a structured neuron population
• Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields
• Bounds and long term convergence for the voltage-conductance kinetic system arising in neuroscience

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