Analysis and numerical solver for excitatory-inhibitory networks with delay and refractory periods
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Publication:4631390
DOI10.1051/m2an/2018014zbMath1411.35178arXiv1705.02205OpenAlexW2793196578MaRDI QIDQ4631390
Maria José Cáceres, Ricarda Schneider
Publication date: 24 April 2019
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1705.02205
entropynoiseneural networksblow-uplong time behaviorsteady statesleaky integrate and fire modelstransmission delayrefractory states
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Cites Work
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- On a kinetic FitzHugh-Nagumo model of neuronal network
- Theoretical connections between mathematical neuronal models corresponding to different expressions of noise
- Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model
- Population density models of integrate-and-fire neurons with jumps: well-posedness
- Synchronization of an excitatory integrate-and-fire neural network
- Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation
- Blow-up, steady states and long time behaviour of excitatory-inhibitory nonlinear neuron models
- On the dynamics of random neuronal networks
- A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics
- Spatially extended networks with singular multi-scale connectivity patterns
- Dynamics of current-based, Poisson driven, integrate-and-fire neuronal networks
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- The Fokker-Planck equation. Methods of solution and applications.
- Statistical model of the hippocampal CA3 region. II: The population framework: Model of rhythmic activity in the CA3 slice
- A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application in orientation tuning
- On the simulation of large populations of neurons.
- Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.
- Mean-field limit of generalized Hawkes processes
- A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods.
- Efficient implementation of weighted ENO schemes
- Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
- Analysis of nonlinear noisy integrate \& fire neuron models: blow-up and steady states
- Particle systems with a singular mean-field self-excitation. Application to neuronal networks
- Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
- A model for feature linking via collective oscillations in the primary visual cortex
- On a voltage-conductance kinetic system for integrate \& fire neural networks
- Propagation of chaos in neural fields
- 2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods
- Beyond blow-up in excitatory integrate and fire neuronal networks: refractory period and spontaneous activity
- Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size
- Relaxation and Self-Sustained Oscillations in the Time Elapsed Neuron Network Model
- Dynamics of the Firing Probability of Noisy Integrate-and-Fire Neurons
- Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience
- Microscopic approach of a time elapsed neural model
- Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models
- Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons
- Introduction to Theoretical Neurobiology
- Mean-field analysis of neuronal spike dynamics
- Dynamics of Globally Coupled Noisy Excitable Elements: The Fitzhugh-Nagumo Case
- Spiking Neuron Models
- A Population Density Approach That Facilitates Large-Scale Modeling of Neural Networks: Extension to Slow Inhibitory Synapses
- Classical Solutions for a Nonlinear Fokker-Planck Equation Arising in Computational Neuroscience
- A theoretical connection between the Noisy Leaky integrate-and-fire and the escape rate models: The non-autonomous case
- The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states
- Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model
- Dynamics of a structured neuron population
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