论文标题
集成和火神经元的平均场模型：固定溶液的非线性稳定性
A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions
论文作者
论文摘要
我们研究了一个由集成和开火的尖峰神经元组成的随机网络，重点是其平均场渐近学。我们考虑McKean-Vlasov方程的不变概率度量，并建立明确的足够条件，以确保此不变分布的局部稳定性。此外，我们证明了J. Touboul和P. Robert最初提出的关于该神经元模型的特定实例的可行性质。
We investigate a stochastic network composed of Integrate-and-Fire spiking neurons, focusing on its mean-field asymptotics. We consider an invariant probability measure of the McKean-Vlasov equation and establish an explicit sufficient condition to ensure the local stability of this invariant distribution. Furthermore, we prove a conjecture proposed initially by J. Touboul and P. Robert regarding the bistable nature of a specific instance of this neuronal model.
