神经元爆发调制的奇点理论模型
Modeling the modulation of neuronal bursting: a singularity theory approach
摘要：
利用神经元电导模型的特殊结构，研究了神经元爆发调制的数学建模。该方法结合奇异性理论和几何奇异扰动来刻画高余维奇异点附近多时间尺度吸引子的几何结构。我们检测到一个三个时间尺度爆裂吸引子的普遍展开的翼尖奇异性和讨论的生理相关性的分歧和展开参数，在确定生理调制爆裂。结果表明，一般性和简单的组织作用的翼尖奇异性的全球动态的电导为基础的模型。
英文摘要：
Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations to capture the geometry of multiple time-scales attractors in the neighborhood of high-codimension singularities. We detect a three-time scale bursting attractor in the universal unfolding of the winged cusp singularity and discuss the physiological relevance of the bifurcation and unfolding parameters in determining a physiological modulation of bursting. The results suggest generality and simplicity in the organizing role of the winged cusp singularity for the global dynamics of conductance based models.
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