Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, U.S.A.
Neural Comput. 2012 Aug;24(8):2078-118. doi: 10.1162/NECO_a_00308. Epub 2012 Apr 17.
We study the dynamics of a quadratic integrate-and-fire model of a single-compartment neuron with a slow recovery variable, as input current and parameters describing timescales, recovery variable, and postspike reset change. Analysis of a codimension 2 bifurcation reveals that the domain of attraction of a stable hyperpolarized rest state interacts subtly with reset parameters, which reposition the system state after spiking. We obtain explicit approximations of instantaneous firing rates for fixed values of the recovery variable, and use the averaging theorem to obtain asymptotic firing rates as a function of current and reset parameters. Along with the different phase-plane geometries, these computations provide explicit tools for the interpretation of different spiking patterns and guide parameter selection in modeling different cortical cell types.
我们研究了具有慢恢复变量的单室神经元的二次积分和点火模型的动力学，其中输入电流和描述时间尺度、恢复变量和峰后重置的参数发生了变化。对余维 2 分岔的分析表明，稳定的超极化静息状态的吸引域与重置参数微妙地相互作用，在峰后重新定位系统状态。我们获得了恢复变量固定值时瞬时点火率的显式近似值，并使用平均定理获得了作为电流和重置参数的函数的渐近点火率。除了不同的相平面几何形状，这些计算还为解释不同的脉冲模式提供了显式工具，并指导在建模不同皮质细胞类型时选择参数。
