Long Time Behavior of an Age- and Leaky Memory-Structured Neuronal Population Equation
DOI10.1137/21M1428571zbMath1496.35075arXiv2106.11110OpenAlexW3175513262MaRDI QIDQ5101328
Valentin Schmutz, Claudia Fonte
Publication date: 30 August 2022
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2106.11110
spiking neuronspike-frequency adaptationpiecewise deterministic Markov processmean-field equationshort-term synaptic plasticitynonlocal transport equationDoeblin's and Harris's theorems
Asymptotic behavior of solutions to PDEs (35B40) Neural networks for/in biological studies, artificial life and related topics (92B20) Nonlinear first-order PDEs (35F20) Boundary value problems for linear first-order PDEs (35F15) Transport equations (35Q49)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation
- On a toy model of interacting neurons
- On the simulation of large populations of neurons.
- Weak and strong connectivity regimes for a general time elapsed neuron network model
- Mean-field limit of generalized Hawkes processes
- Relaxation in time elapsed neuron network models in the weak connectivity regime
- Mean-field limit of age and leaky memory dependent Hawkes processes
- Exponential stability of the stationary distribution of a mean field of spiking neural network
- Hopf bifurcation in a mean-field model of spiking neurons
- Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions
- Long time behavior of a mean-field model of interacting neurons
- Hydrodynamic limit for interacting neurons
- Mean-field analysis of selective persistent activity in presence of short-term synaptic depression
- Predicting spike timing of neocortical pyramidal neurons by simple threshold models
- Frequency-dependent response properties of adapting spiking neurons
- Patterns of Synchrony in Neural Networks with Spike Adaptation
- Relaxation and Self-Sustained Oscillations in the Time Elapsed Neuron Network Model
- 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
- Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
- A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation
- Asymptotic behaviour of neuron population models structured by elapsed-time
- Measure Solutions To The Conservative Renewal Equation
- A Universal Model for Spike-Frequency Adaptation
- The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states
- NEURAL EXCITABILITY, SPIKING AND BURSTING
- Éléments d'une théorie générale des chaînes simples constantes de Markoff
- Dynamics of a structured neuron population
- Stability, convergence to equilibrium and simulation of non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels
This page was built for publication: Long Time Behavior of an Age- and Leaky Memory-Structured Neuronal Population Equation
