论文标题
Fitzhugh-Nagumo神经网络中的浓度曲线：一种HOPF-COLE方法
Concentration profiles in FitzHugh-Nagumo neural networks: A Hopf-Cole approach
论文作者
论文摘要
在本文中，我们着重于具有相互作用的空间扩展的Fitzhugh-Nagumo模型。在强烈和局部相互作用占主导地位的制度中，我们量化了神经元的概率密度如何集中到狄拉克分布中。先前调查此问题的工作提供了可集成性空间的相对界限。使用HOPF-COLE框架，我们使用微妙的显式子和超级解决方案来得出精确的$ l^\ infty $估计，这些解决方案证明，随着收敛速度，吹动的配置文件是高斯。
In this paper we focus on a spatially extended FitzHugh-Nagumo model with interactions. In the regime where strong and local interactions dominate, we quantify how the probability density of neurons concentrates into a Dirac distribution. Previous work investigating this question have provided relative bounds in integrability spaces. Using a Hopf-Cole framework, we derive precise $L^\infty$ estimates using subtle explicit sub- and super- solutions which prove, with rates of convergence, that the blow up profile is Gaussian.
