Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations
Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations
复制标题
一些神经场方程的平稳解的局部/全局分析
DOI：
10.1137/090773611
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
O. Faugeras
中科院分区：
文献类型：
--
作者：
R. Veltz;O. Faugeras
神经场或皮质场是中观模型的连续集合，也称为神经团块，是对大脑宏观部分进行建模的基础。神经场用非线性积分-微分方程组来描述。这些方程的解代表了这些群体在接受来自邻近大脑区域的输入时的活动状态。了解这些解决方案的性质对于促进我们对大脑的理解是至关重要的。本文研究了神经场方程的定常解对非线性的刚度和外部输入的对比度的依赖性。这是通过在泛函空间，特别是无限维空间中使用度理论和分支理论来完成的。这两个理论的联合使用使我们能够对解的全局和局部行为做出新的详细预测。我们还给出了一个通用的有限维应用程序。
Neural or cortical fields are continuous assemblies of mesoscopic models, also called neural masses, of neural populations that are fundamental in the modeling of macroscopic parts of the brain. Neural fields are described by nonlinear integro-differential equations. The solutions of these equations represent the state of activity of these populations when submitted to inputs from neighboring brain areas. Understanding the properties of these solutions is essential to advancing our understanding of the brain. In this paper we study the dependency of the stationary solutions of the neural fields equations with respect to the stiffness of the nonlinearity and the contrast of the external inputs. This is done by using degree theory and bifurcation theory in the context of functional, in particular, infinite dimensional, spaces. The joint use of these two theories allows us to make new detailed predictions about the global and local behaviors of the solutions. We also provide a generic finite dimensional appr...
DOI：
10.1098/rstb.2000.0769
发表时间：
2001-03-29
影响因子：
6.3
作者：
Bressloff, PC;Cowan, JD;Wiener, MC
通讯作者：
Wiener, MC