Exponential stability of the stationary distribution of a mean field of spiking neural network
From MaRDI portal
Publication:2208458
DOI10.1016/j.jde.2020.08.001zbMath1451.35025OpenAlexW2735178964MaRDI QIDQ2208458
Publication date: 3 November 2020
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://hal.inria.fr/hal-01290264v2/file/rapport-hal.pdf
Asymptotic behavior of solutions to PDEs (35B40) Neural networks for/in biological studies, artificial life and related topics (92B20) Integro-partial differential equations (35R09) Transport equations (35Q49)
Related Items
Long Time Behavior of an Age- and Leaky Memory-Structured Neuronal Population Equation ⋮ Can the Clocks Tick Together Despite the Noise? Stochastic Simulations and Analysis ⋮ Sampled-data-based exponential synchronization of switched coupled neural networks with unbounded delay
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On a toy model of interacting neurons
- Positive operator semigroups. From finite to infinite dimensions
- On the dynamics of random neuronal networks
- Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
- Hydrodynamic limit for spatially structured interacting neurons
- Semigroups of linear operators and applications to partial differential equations
- Boundary value problems in abstract kinetic theory
- Über das Spektrum positiver Generatoren
- Mean-field limit of generalized Hawkes processes
- Relaxation in time elapsed neuron network models in the weak connectivity regime
- Non-linear age-dependent population dynamics
- Delay equations. Functional-, complex-, and nonlinear analysis
- Analysis of nonlinear noisy integrate \& fire neuron models: blow-up and steady states
- On local bifurcations in neural field models with transmission delays
- Hydrodynamic limit for interacting neurons
- Particle systems with a singular mean-field self-excitation. Application to neuronal networks
- Multi-class oscillating systems of interacting neurons
- A Center Manifold Result for Delayed Neural Fields Equations
- Relaxation and Self-Sustained Oscillations in the Time Elapsed Neuron Network Model
- Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience
- Stability analysis for equilibria in age-specific population dynamics
- Microscopic approach of a time elapsed neural model
- Cauchy problems with state-dependent time evolution
- One-Parameter Semigroups for Linear Evolution Equations
- Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics