论文标题
Fitzhugh-Nagumo神经网络中的大耦合：定量和强收敛结果
Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results
论文作者
论文摘要
我们考虑了一种用于空间扩展的Fitzhugh-Nagumo神经网络的介观模型，并证明在短程相互作用主导的政权中，整个网络中电势的概率密度集中在dirac分布中，其质量中心求解了经典的非局部非局部反应 - 非局部反应 - 反应 - fitzhugh-Nagugh-nagumo系统。为了完善对这一制度的理解，我们专注于这种浓度现象的爆炸概况。我们这里的主要目的是得出两个定量和强的收敛估计，证明了该轮廓是高斯：L1功能框架中的第一个，而第二个是加权L2功能设置中的第二个。我们开发了原始的相对熵技术来证明第一个结果，而第二个结果依赖于规律性的传播。
We consider a mesoscopic model for a spatially extended FitzHugh-Nagumo neural network and prove that in the regime where short-range interactions dominate, the probability density of the potential throughout the network concentrates into a Dirac distribution whose center of mass solves the classical non-local reaction-diffusion FitzHugh-Nagumo system. In order to refine our comprehension of this regime, we focus on the blow-up profile of this concentration phenomenon. Our main purpose here consists in deriving two quantitative and strong convergence estimates proving that the profile is Gaussian: the first one in a L1 functional framework and the second in a weighted L2 functional setting. We develop original relative entropy techniques to prove the first result whereas our second result relies on propagation of regularity.
