论文标题
神经科学中产生的电压传统动力学系统的边界和长期收敛
Bounds and long term convergence for the voltage-conductance kinetic system arising in neuroscience
论文作者
论文摘要
电压传导方程确定了描述视觉皮层中发生波动驱动的神经元网络的随机过程的概率分布。它的结构和堕落与动力学福克 - 普兰克方程共享许多共同特征，该方程最近引起了很多关注。我们证明了稳态解决方案上的l $ \ infty $以及进化问题向这种固定状态的长期融合。尽管具有低纤维性特性，但困难是处理沿边界变化类型的边界条件。这导致我们在alikakos迭代中使用特定权重，并适应相对熵方法。
The voltage-conductance equation determines the probability distribution of a stochastic process describing a fluctuation-driven neuronal network arising in the visual cortex. Its structure and degeneracy share many common features with the kinetic Fokker-Planck equation, which has attracted much attention recently. We prove an L $\infty$ bound on the steady state solution and the long term convergence of the evolution problem towards this stationary state. Despite the hypoellipticity property, the difficulty is to treat the boundary conditions that change type along the boundary. This leads us to use specific weights in the Alikakos iterations and adapt the relative entropy method.
