Periodic solutions to a mean-field model for electrocortical activity
Periodic solutions to a mean-field model for electrocortical activity
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皮层电活动平均场模型的周期解
DOI：
10.1140/epjst/e2014-02311-y
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
K. R. Green
中科院分区：
文献类型：
--
作者：
L. Veen;K. R. Green
我们考虑一个连续模型的电信号在人类皮层，它采取的形式是一个系统的半线性，双曲偏微分方程的抑制性和兴奋性膜电位和突触输入。这些组件的耦合表示为S形和二次非线性。我们认为这些方程在一个正方形域周期性边界条件，在附近的主要过渡从一个稳定的平衡，时间周期运动通过等变的Hopf分岔。我们计算一族驻波解的一部分，从这一点发出。
We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling of these components is represented by sigmoidal and quadratic nonlinearities. We consider these equations on a square domain with periodic boundary conditions, in the vicinity of the primary transition from a stable equilibrium to time-periodic motion through an equivariant Hopf bifurcation. We compute part of a family of standing wave solutions, emanating from this point.